Art of Problem Solving in Abc Bc Is the Average of the Other Two Sides

Math Models

30 Solve Applications with Linear Inequalities

Learning Objectives

By the terminate of this department, you lot will be able to:

• Solve applications with linear inequalities

Earlier you get started, take this readiness quiz.

1. Write equally an inequality: x is at least 30.
   If you missed this problem, review (Effigy).
2. Solve
   If you missed this problem, review (Figure).

Solve Applications with Linear Inequalities

Many real-life situations crave us to solve inequalities. In fact, inequality applications are so common that we ofttimes practice not even realize we are doing algebra. For example, how many gallons of gas can be put in the motorcar for ?xx? Is the rent on an apartment affordable? Is there plenty time before form to get get lunch, eat it, and return? How much money should each family unit member'southward holiday souvenir toll without going over budget?

The method we will use to solve applications with linear inequalities is very much similar the one we used when nosotros solved applications with equations. We will read the problem and brand sure all the words are understood. Side by side, we will identify what nosotros are looking for and assign a variable to stand for it. We will restate the trouble in one sentence to arrive piece of cake to interpret into an inequality. And then, we volition solve the inequality.

Emma got a new job and volition take to move. Her monthly income will be ?5,265. To qualify to rent an apartment, Emma'south monthly income must be at least 3 times equally much every bit the rent. What is the highest hire Emma will qualify for?

Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet tin safely support no more than than 900 pounds. How many boxes tin can he safely load onto the pallet?

There tin can be no more 20 boxes.

The elevator in Yehire's flat building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people tin can safely ride the elevator?

A maximum of xiv people can safely ride in the elevator.

Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. In that case, we must round the algebraic solution to a whole number. The context of the application will determine whether we circular upwardly or down. To check applications like this, we will circular our answer to a number that is easy to compute with and brand sure that number makes the inequality true.

Dawn won a mini-grant of ?4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost ?254.12 each, including tax and delivery. What is the maximum number of tablets Dawn tin buy?

Angie has ?twenty to spend on juice boxes for her son's preschool picnic. Each pack of juice boxes costs ?2.63. What is the maximum number of packs she can buy?

7 packs

Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost ?42.75 per person for dinner, including tip and revenue enhancement. His upkeep for the political party is ?500. What is the maximum number of people Daniel can accept at the party?

11 people

Pete works at a computer store. His weekly pay will be either a stock-still corporeality, ?925, or ?500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the stock-still amount of ?925?

Tiffany just graduated from college and her new job will pay her ?twenty,000 per yr plus 2% of all sales. She wants to earn at least ?100,000 per year. For what total sales will she be able to achieve her goal?

at to the lowest degree ?four,000,000

Christian has been offered a new job that pays ?24,000 a twelvemonth plus 3% of sales. For what total sales would this new job pay more his current task which pays ?60,000?

at least ?1,200,000

Sergio and Lizeth take a very tight vacation budget. They plan to hire a car from a company that charges ?75 a calendar week plus ?0.25 a mile. How many miles can they travel and still proceed within their ?200 budget?

Taleisha's phone plan costs her ?28.80 a month plus ?0.twenty per text message. How many text messages can she use and go along her monthly phone bill no more than ?50?

no more than 106 text messages

Rameen's heating bill is ?5.42 per month plus ?one.08 per therm. How many therms tin can Rameen use if he wants his heating beak to be a maximum of ?87.50?

no more than than 76 therms

A mutual goal of well-nigh businesses is to brand a profit. Profit is the coin that remains when the expenses take been subtracted from the money earned. In the next example, we will find the number of jobs a minor businessman needs to do every month in order to make a certain corporeality of profit.

Elliot has a mural maintenance business organisation. His monthly expenses are ?one,100. If he charges ?threescore per job, how many jobs must he exercise to earn a profit of at least ?4,000 a month?

Caleb has a pet sitting business. He charges ?32 per 60 minutes. His monthly expenses are ?ii,272. How many hours must he work in guild to earn a turn a profit of at least ?800 per calendar month?

at least 96 hours

Felicity has a calligraphy business. She charges ?2.50 per wedding invitation. Her monthly expenses are ?650. How many invitations must she write to earn a profit of at least ?2,800 per month?

at least i,380 invitations

Sometimes life gets complicated! There are many situations in which several quantities contribute to the total expense. We must make sure to business relationship for all the individual expenses when we solve issues like this.

Brenda's best friend is having a destination wedding and the upshot will terminal 3 days. Brenda has ?500 in savings and can earn ?15 an hour babysitting. She expects to pay ?350 airfare, ?375 for food and entertainment and ?60 a nighttime for her share of a hotel room. How many hours must she babysit to take plenty money to pay for the trip?

Malik is planning a vi-day summer vacation trip. He has ?840 in savings, and he earns ?45 per hour for tutoring. The trip volition cost him ?525 for airfare, ?780 for food and sightseeing, and ?95 per night for the hotel. How many hours must he tutor to accept enough money to pay for the trip?

at least 23 hours

Josue wants to go on a 10-24-hour interval road trip side by side spring. It will cost him ?180 for gas, ?450 for food, and ?49 per night for a motel. He has ?520 in savings and can earn ?30 per driveway shoveling snowfall. How many driveways must he shovel to have plenty money to pay for the trip?

at to the lowest degree 20 driveways

Cardinal Concepts

• Solving inequalities
  1. Read the problem.
  2. Identify what we are looking for.
  3. Proper name what nosotros are looking for. Choose a variable to stand for that quantity.
  4. Translate. Write a sentence that gives the information to find it. Interpret into an inequality.
  5. Solve the inequality.
  6. Check the respond in the trouble and brand sure it makes sense.
  7. Answer the question with a complete sentence.

Section Exercises

Practice Makes Perfect

Solve Applications with Linear Inequalities

In the following exercises, solve.

Mona is planning her son's altogether party and has a budget of ?285. The Fun Zone charges ?19 per child. How many children can she have at the party and stay within her upkeep?

fifteen children

Carlos is looking at apartments with 3 of his friends. They want the monthly rent to be no more ?2360. If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay?

A water taxi has a maximum load of one,800 pounds. If the boilerplate weight of one person is 150 pounds, how many people can safely ride in the water taxi?

12 people

Marcela is registering for her college classes, which cost ?105 per unit of measurement. How many units can she take to take a maximum cost of ?1,365?

Arleen got a ?20 souvenir carte du jour for the coffee store. Her favorite iced drink costs ?3.79. What is the maximum number of drinks she tin buy with the gift bill of fare?

five drinks

Teegan likes to play golf game. He has budgeted ?threescore next month for the driving range. It costs him ?10.55 for a bucket of assurance each fourth dimension he goes. What is the maximum number of times he tin go to the driving range next month?

Joni sells kitchen aprons online for ?32.50 each. How many aprons must she sell side by side month if she wants to earn at least ?1,000?

31 aprons

Ryan charges his neighbors ?17.50 to wash their car. How many cars must he wash next summer if his goal is to earn at least ?ane,500?

Keshad gets paid ?2,400 per month plus six% of his sales. His brother earns ?iii,300 per calendar month. For what amount of total sales will Keshad's monthly pay exist higher than his brother's monthly pay?

?fifteen,000

Kimuyen needs to earn ?four,150 per calendar month in society to pay all her expenses. Her job pays her ?3,475 per calendar month plus iv% of her total sales. What is the minimum Kimuyen's total sales must be in social club for her to pay all her expenses?

Andre has been offered an entry-level job. The company offered him ?48,000 per year plus 3.5% of his total sales. Andre knows that the boilerplate pay for this job is ?62,000. What would Andre'south total sales demand to be for his pay to be at least every bit loftier as the average pay for this chore?

?400,000

Nataly is considering 2 job offers. The first job would pay her ?83,000 per year. The second would pay her ?66,500 plus 15% of her total sales. What would her total sales demand to be for her salary on the second offering be higher than the first?

Jake'southward water beak is ?24.lxxx per month plus ?two.xx per ccf (hundred cubic feet) of water. What is the maximum number of ccf Jake tin can apply if he wants his bill to be no more ?threescore?

16 ccf

Kiyoshi'due south phone plan costs ?17.fifty per month plus ?0.15 per text message. What is the maximum number of text messages Kiyoshi can utilize so the phone pecker is no more than ?56.l?

Marlon'southward Tv plan costs ?49.99 per month plus ?5.49 per first-run movie. How many commencement-run movies can he sentinel if he wants to continue his monthly pecker to be a maximum of ?100?

9 movies

Kellen wants to rent a banquet room in a restaurant for her cousin'due south baby shower. The restaurant charges ?350 for the banquet room plus ?32.50 per person for lunch. How many people can Kellen take at the shower if she wants the maximum price to be ?1,500?

Moshde runs a hairstyling business from her business firm. She charges ?45 for a haircut and style. Her monthly expenses are ?960. She wants to be able to put at least ?1,200 per month into her savings account society to open up her own salon. How many "cutting & styles" must she do to save at to the lowest degree ?1,200 per month?

48 cut & styles

Noe installs and configures software on dwelling house computers. He charges ?125 per task. His monthly expenses are ?ane,600. How many jobs must he work in order to make a profit of at least ?2,400?

Katherine is a personal chef. She charges ?115 per four-person meal. Her monthly expenses are ?3,150. How many iv-person meals must she sell in society to make a turn a profit of at least ?ane,900?

44 meals

Melissa makes necklaces and sells them online. She charges ?88 per necklace. Her monthly expenses are ?3745. How many necklaces must she sell if she wants to make a profit of at least ?1,650?

V student authorities officers want to get to the state convention. It will cost them ?110 for registration, ?375 for transportation and food, and ?42 per person for the hotel. There is ?450 budgeted for the convention in the student government savings account. They can earn the rest of the coin they need by having a auto launder. If they accuse ?5 per car, how many cars must they wash in club to have enough money to pay for the trip?

49 cars

Cesar is planning a 4-twenty-four hours trip to visit his friend at a higher in another country. It will cost him ?198 for airfare, ?56 for local transportation, and ?45 per day for food. He has ?189 in savings and can earn ?35 for each lawn he mows. How many lawns must he mow to have enough money to pay for the trip?

Alonzo works as a motorcar detailer. He charges ?175 per car. He is planning to movement out of his parents' firm and rent his first apartment. He volition demand to pay ?120 for application fees, ?950 for security deposit, and showtime and last months' rent at ?ane,140 per calendar month. He has ?1,810 in savings. How many cars must he detail to accept enough coin to rent the apartment?

ix cars

Eun-Kyung works as a tutor and earns ?threescore per 60 minutes. She has ?792 in savings. She is planning an anniversary party for her parents. She would like to invite forty guests. The party will cost her ?1,520 for nutrient and drinks and ?150 for the photographer. She volition also have a favor for each of the guests, and each favor will toll ?vii.l. How many hours must she tutor to have enough money for the party?

Everyday Math

Maximum Load on a Stage In 2014, a high schoolhouse stage complanate in Fullerton, California, when 250 students got on stage for the finale of a musical production. Ii dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a educatee is assumed to exist 140 pounds, what is the maximum number of students who could safely be on the stage?

91 students

Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?

Wedding ceremony Budget Adele and Walter found the perfect venue for their wedding reception. The price is ?nine,850 for upwardly to 100 guests, plus ?38 for each additional guest. How many guests tin can attend if Adele and Walter desire the total cost to be no more than ?12,500?

169 guests

Shower Upkeep Penny is planning a infant shower for her daughter-in-law. The restaurant charges ?950 for up to 25 guests, plus ?31.95 for each additional guest. How many guests tin attend if Penny wants the total price to be no more than ?ane,500?

Writing Exercises

Find your concluding calendar month'southward telephone neb and the hourly salary yous are paid at your chore. (If you exercise not take a job, apply the hourly bacon you lot would realistically be paid if you lot had a job.) Calculate the number of hours of work it would take yous to earn at to the lowest degree enough money to pay your phone bill by writing an appropriate inequality and then solving it.

Answers will vary.

Find out how many units you have left, after this term, to attain your college goal and approximate the number of units you tin can take each term in college. Summate the number of terms it will take you to achieve your college goal past writing an appropriate inequality and so solving it.

Self Bank check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ What does this checklist tell yous near your mastery of this section? What steps volition you take to meliorate?

Chapter 3 Review Exercises

3.1 Using a Trouble Solving Strategy

Approach Give-and-take Bug with a Positive Attitude

In the post-obit exercises, reflect on your arroyo to give-and-take problems.

How has your attitude towards solving discussion bug changed as a effect of working through this chapter? Explain.

answers will vary

Did the problem-solving strategy help you solve discussion problems in this chapter? Explain.

Employ a Problem-Solving Strategy for Word Problems

In the following exercises, solve using the problem-solving strategy for discussion problems. Remember to write a complete sentence to respond each question.

Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?

116

There are nine saxophone players in the band. The number of saxophone players is 1 less than twice the number of tuba players. Find the number of tuba players.

Solve Number Issues

In the post-obit exercises, solve each number word problem.

The sum of a number and three is xl-one. Discover the number.

38

Twice the difference of a number and ten is fifty-four. Find the number.

One number is 9 less than another. Their sum is negative twenty-vii. Detect the numbers.

I number is 11 more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.

1 number is two more than than four times another. Their sum is Notice the numbers.

The sum of two consecutive integers is Find the numbers.

Find three consecutive integers whose sum is

Find three consecutive even integers whose sum is 234.

Find three consecutive odd integers whose sum is 51.

fifteen, 17, 19

Koji has ?v,502 in his savings account. This is ?30 less than six times the corporeality in his checking account. How much money does Koji have in his checking business relationship?

three.2 Solve Percent Applications

Translate and Solve Bones Percent Equations

In the following exercises, interpret and solve.

What number is 67% of 250?

167.5

300% of 82 is what number?

12.5% of what number is xx?

160

72 is thirty% of what number?

What percent of 125 is 150?

120%

127.5 is what percent of 850?

Solve Percent Applications

In the post-obit exercises, solve.

The bill for Dino's lunch was ?19.45. He wanted to exit twenty% of the total bill equally a tip. How much should the tip be?

?3.89

Reza was very sick and lost 15% of his original weight. He lost 27 pounds. What was his original weight?

Dolores bought a crib on auction for ?350. The sale price was 40% of the original price. What was the original price of the crib?

?875

Jaden earns ?two,680 per month. He pays ?938 a calendar month for rent. What percent of his monthly pay goes to hire?

Observe Percent Increase and Percent Decrease

In the following exercises, solve.

Angel'southward got a heighten in his almanac salary from ?55,400 to ?56,785. Find the per centum increase.

ii.5%

Rowena's monthly gasoline bill dropped from ?83.75 last month to ?56.95 this calendar month. Find the per centum decrease.

Solve Elementary Interest Applications

In the following exercises, solve.

Winston deposited ?3,294 in a bank account with interest rate 2.6%. How much interest was earned in v years?

?428.22

Moira borrowed ?4,500 from her grandfather to pay for her first year of higher. Iii years subsequently, she repaid the ?4,500 plus ?243 involvement. What was the rate of interest?

Jaime's fridge loan statement said he would pay ?ane,026 in involvement for a four-year loan at 13.5%. How much did Jaime borrow to buy the refrigerator?

?1,900

In 12 years, a bail that paid six.35% involvement earned ?seven,620 interest. What was the principal of the bond?

Solve Applications with Discount or Mark-up

In the following exercises, detect the sale price.

The original price of a handbag was ?84. Carole bought information technology on sale for ?21 off.

?63

Marian wants to purchase a java table that costs ?495. Next week the java table will be on sale for ?149 off.

In the following exercises, find ⓐ the amount of discount and ⓑ the auction price.

Emmett bought a pair of shoes on auction at forty% off from an original cost of ?138.

ⓐ ?55.20 ⓑ ?82.80

Anastasia bought a dress on sale at 75% off from an original price of ?280.

In the following exercises, find ⓐ the corporeality of disbelieve and ⓑ the disbelieve rate. (Circular to the nearest tenth of a percentage, if needed.)

Zack bought a printer for his office that was on auction for ?380. The original price of the printer was ?450.

ⓐ ?lxx ⓑ 15.6%

Lacey bought a pair of boots on auction for ?95. The original price of the boots was ?200.

In the post-obit exercises, detect ⓐ the corporeality of the mark-up and ⓑ the list cost.

Nga and Lauren bought a chest at a flea market for ?fifty. They re-finished information technology then added a 350% marker-up.

ⓐ ?175 ⓑ ?225

Carly bought bottled water for ?0.24 per bottle at the disbelieve store. She added a 75% mark-up before selling them at the football game game.

three.3 Solve Mixture Applications

Solve Coin Word Problems

In the post-obit exercises, solve each coin give-and-take problem.

Francie has ?4.35 in dimes and quarters. The number of dimes is five more than than the number of quarters. How many of each coin does she take?

16 dimes, eleven quarters

Scott has ?0.39 in pennies and nickels. The number of pennies is viii times the number of nickels. How many of each coin does he have?

Paulette has ?140 in ?5 and ?10 bills. The number of ?x bills is one less than twice the number of ?5 bills. How many of each does she accept?

six ?five bills, eleven ?10 bills

Lenny has ?3.69 in pennies, dimes, and quarters. The number of pennies is three more than than the number of dimes. The number of quarters is twice the number of dimes. How many of each money does he have?

Solve Ticket and Stamp Word Problems

In the following exercises, solve each ticket or stamp discussion trouble.

A church building tiffin made ?842. Adult tickets toll ?x each and children's tickets cost ?6 each. The number of children was 12 more than twice the number of adults. How many of each ticket were sold?

35 adults, 82 children

Tickets for a basketball game cost ?2 for students and ?5 for adults. The number of students was 3 less than 10 times the number of adults. The full amount of money from ticket sales was ?619. How many of each ticket were sold?

125 tickets were sold for the jazz band concert for a full of ?1,022. Student tickets toll ?6 each and general access tickets cost ?10 each. How many of each kind of ticket were sold?

57 students, 68 adults

One afternoon the water park sold 525 tickets for a total of ?xiii,545. Child tickets cost ?xix each and developed tickets cost ?40 each. How many of each kind of ticket were sold?

Ana spent ?4.06 buying stamps. The number of ?0.41 stamps she bought was 5 more than the number of ?0.26 stamps. How many of each did she buy?

3 ?0.26 stamps, eight ?0.41 stamps

Yumi spent ?34.15 buying stamps. The number of ?0.56 stamps she bought was 10 less than four times the number of ?0.41 stamps. How many of each did she buy?

Solve Mixture Give-and-take Issues

In the following exercises, solve each mixture word problem.

Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins price ?3.45 per pound and nuts cost ?7.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese apply for the trail mix to price him ?half-dozen.96 per pound?

ii.two lb. of raisins, 7.8 lb. of nuts

Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tile. She will utilize basic tiles that toll ?8 per square pes and decorator tiles that toll ?20 per foursquare human foot. How many square feet of each tile should she use and then that the overall cost of the backsplash will be ?x per foursquare foot?

Shawn has ?15,000 to invest. She will put some of it into a fund that pays 4.5% almanac interest and the rest in a certificate of deposit that pays one.8% annual interest. How much should she invest in each account if she wants to earn 4.05% annual involvement on the full corporeality?

?12,500 at iv.5%, ?2,500 at 1.8%

Enrique borrowed ?23,500 to buy a car. He pays his uncle two% interest on the ?4,500 he borrowed from him, and he pays the depository financial institution 11.five% involvement on the rest. What average interest rate does he pay on the full ?23,500? (Round your respond to the nearest tenth of a percent.)

3.iv Solve Geometry Applications: Triangles, Rectangles and the Pythagorean Theorem

Solve Applications Using Triangle Properties

In the following exercises, solve using triangle backdrop.

The measures of two angles of a triangle are 22 and 85 degrees. Find the measure of the tertiary angle.

The playground at a shopping mall is a triangle with perimeter 48 feet. The lengths of ii sides are xix feet and fourteen feet. How long is the 3rd side?

A triangular road sign has base of operations 30 inches and height 40 inches. What is its expanse?

600 square inches

What is the pinnacle of a triangle with surface area 67.5 foursquare meters and base of operations 9 meters?

One angle of a triangle is more than the smallest angle. The largest angle is the sum of the other angles. Detect the measures of all three angles.

One angle of a right triangle measures What is the measure of the other angles of the triangle?

The measure of the smallest angle in a right triangle is less than the measure of the adjacent larger angle. Observe the measures of all three angles.

The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more than the smallest side. The third side is half-dozen feet more than twice the smallest side. Find the lengths of all sides.

Use the Pythagorean Theorem

In the following exercises, apply the Pythagorean Theorem to find the length of the hypotenuse.

26

In the following exercises, use the Pythagorean Theorem to observe the length of the missing side. Round to the nearest tenth, if necessary.

8

viii.1

In the following exercises, solve. Judge to the nearest tenth, if necessary.

Sergio needs to attach a wire to agree the antenna to the roof of his house, as shown in the figure. The antenna is 8 feet tall and Sergio has 10 anxiety of wire. How far from the base of operations of the antenna can he attach the wire?

Seong is building shelving in his garage. The shelves are 36 inches wide and 15 inches tall. He wants to put a diagonal brace across the dorsum to stabilize the shelves, as shown. How long should the brace exist?

Solve Applications Using Rectangle Properties

In the following exercises, solve using rectangle properties.

The length of a rectangle is 36 feet and the width is 19 feet. Find the ⓐ perimeter ⓑ area.

ⓐ 110 ft. ⓑ 684 sq. ft.

A sidewalk in front of Kathy's business firm is in the shape of a rectangle four feet wide by 45 anxiety long. Detect the ⓐ perimeter ⓑ surface area.

The expanse of a rectangle is 2356 foursquare meters. The length is 38 meters. What is the width?

62 m

The width of a rectangle is 45 centimeters. The expanse is ii,700 square centimeters. What is the length?

The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Detect the length and the width.

24.5 cm, 12.5 cm

The width of a rectangle is 3 more than twice the length. The perimeter is 96 inches. Find the length and the width.

three.5 Solve Uniform Motion Applications

Solve Uniform Motility Applications

In the post-obit exercises, solve.

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa two hours to drive the same distance. Elsa's speed is vii miles per hour faster than Gabe'south speed. Find Gabe'due south speed and Elsa's speed.

Gabe 70 mph, Elsa 77 mph

Louellen and Tracy met at a restaurant on the road between Chicago and Nashville. Louellen had left Chicago and drove 3.2 hours towards Nashville. Tracy had left Nashville and collection 4 hours towards Chicago, at a speed i mile per hr faster than Louellen's speed. The distance betwixt Chicago and Nashville is 472 miles. Detect Louellen'due south speed and Tracy's speed.

Ii busses leave Amarillo at the same time. The Albuquerque bus heads w on the I-40 at a speed of 72 miles per hour, and the Oklahoma Urban center bus heads e on the I-forty at a speed of 78 miles per 60 minutes. How many hours will it take them to be 375 miles apart?

2.five hours

Kyle rowed his boat upstream for 50 minutes. It took him thirty minutes to row back downstream. His speed going upstream is 2 miles per hour slower than his speed going downstream. Notice Kyle's upstream and downstream speeds.

At 6:thirty, Devon left her house and rode her bike on the flat road until 7:xxx. And so she started riding uphill and rode until 8:00. She rode a full of fifteen miles. Her speed on the flat road was 3 miles per hour faster than her speed going uphill. Find Devon'southward speed on the flat road and riding uphill.

apartment road 11 mph, uphill 8 mph

Anthony collection from New York Urban center to Baltimore, a altitude of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was light for the rest of the bulldoze, and he arrived at 7:thirty. His speed in calorie-free traffic was 4 miles per hr more twice his speed in heavy traffic. Find Anthony's driving speed in heavy traffic and calorie-free traffic.

3.half-dozen Solve Applications with Linear Inequalities

Solve Applications with Linear Inequalities

In the post-obit exercises, solve.

Julianne has a weekly food budget of ?231 for her family. If she plans to budget the aforementioned amount for each of the seven days of the calendar week, what is the maximum amount she tin can spend on food each day?

?33 per twenty-four hour period

Rogelio paints watercolors. He got a ?100 souvenir carte to the fine art supply store and wants to utilize information technology to buy canvases. Each canvass costs ?ten.99. What is the maximum number of canvases he can buy with his souvenir carte du jour?

Briana has been offered a sales task in some other city. The offer was for ?42,500 plus 8% of her full sales. In order to make it worth the motility, Briana needs to accept an annual salary of at least ?66,500. What would her total sales need to be for her to motion?

at least ?300,000

Renee's car costs her ?195 per month plus ?0.09 per mile. How many miles tin Renee drive so that her monthly car expenses are no more than ?250?

Costa is an accountant. During tax season, he charges ?125 to practice a simple tax return. His expenses for ownership software, renting an role, and advert are ?6,000. How many tax returns must he do if he wants to make a profit of at least ?8,000?

at least 112 jobs

Jenna is planning a five-24-hour interval resort holiday with three of her friends. It will cost her ?279 for airfare, ?300 for food and entertainment, and ?65 per twenty-four hour period for her share of the hotel. She has ?550 saved towards her vacation and can earn ?25 per hour every bit an banana in her uncle's photography studio. How many hours must she work in order to have enough money for her holiday?

Practice Test

Four-fifths of the people on a hike are children. If there are 12 children, what is the full number of people on the hike?

xv

Ane number is 3 more than twice another. Their sum is Find the numbers.

The sum of two sequent odd integers is Detect the numbers.

Marla'south breakfast was 525 calories. This was 35% of her total calories for the day. How many calories did she have that solar day?

Humberto's hourly pay increased from ?xvi.25 to ?17.55. Find the percent increase.

8%

Melinda deposited ?v,985 in a bank account with an interest rate of 1.9%. How much interest was earned in 2 years?

Dotty bought a freezer on sale for ?486.l. The original toll of the freezer was ?695. Observe ⓐ the amount of discount and ⓑ the discount rate.

ⓐ ?208.50 ⓑ thirty%

Bonita has ?ii.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have?

At a concert, ?1,600 in tickets were sold. Adult tickets were ?nine each and children's tickets were ?4 each. If the number of adult tickets was thirty less than twice the number of children'southward tickets, how many of each kind were sold?

140 adult, 85 children

Kim is making eight gallons of dial from fruit juice and soda. The fruit juice costs ?6.04 per gallon and the soda costs ?4.28 per gallon. How much fruit juice and how much soda should she utilise so that the punch costs ?5.71 per gallon?

The measure of ane angle of a triangle is twice the measure of the smallest angle. The measure of the third bending is 14 more than the mensurate of the smallest angle. Notice the measures of all three angles.

What is the top of a triangle with expanse 277.two foursquare inches and base 44 inches?

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest 10th, if necessary.

10

A baseball diamond is really a square with sides of ninety feet. How far is information technology from abode plate to second base, as shown?

127.three ft.

The length of a rectangle is two feet more than five times the width. The perimeter is xl feet. Find the dimensions of the rectangle.

Two planes leave Dallas at the same fourth dimension. One heads east at a speed of 428 miles per hr. The other plane heads west at a speed of 382 miles per hr. How many hours will it take them to be two,025 miles autonomously?

2.v hours

Leon drove from his house in Cincinnati to his sister's house in Cleveland, a distance of 252 miles. It took him hours. For the kickoff half hr he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?

Chloe has a upkeep of ?800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?

at nearly ?44.44 per costume

Frank constitute a rental car deal online for ?49 per week plus ?0.24 per mile. How many miles could he bulldoze if he wants the full price for one week to be no more than than ?150?

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Source: https://opentextbc.ca/elementaryalgebraopenstax/chapter/solve-applications-with-linear-inequalities/

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