Mathacle PSet Algebra Word Problems ( ) Level Number Name: Date:

Transcription

1 Translate each problem into an equation. Then solve the equation. 1.) Howard works an 8-hour day at his gas station. He spends twice as much time working on cars as he does waiting on customers. He takes 1 ¼ hours to eat lunch and balance his books. How many hours does he spend waiting on customers? 2.) Arthur weighs 34 lb more than Lily. Their combined weight is 180 lb less than four times Lily s weight. How much does Arthur weigh? 3.) Nick worked 16 hours last week. He earned $5 per hour at a local restaurant and $5.50 per hour at a grocery store. If he earned a total of $82, how many hours did he work at the grocery store? 4.) In the game of basketball you can score one point for a foul shot, two points for a regular shot and three points for an outside shot. Manuel scored 30 points by making eight foul shots and two outside shots. How many regular shots did he make? 5.) Three times a number increased by 44 is the same as the opposite of the number. Find the number. 6.) Sean weighs 10 lb more than twice Brad s weight. If Brad gains 10 lb and Sean s weight stays the same, together they will weigh 230 lb. How much does each weigh now?

2 7.) When Courtney collected her change she realized that she had five times as many dimes as quarters. Her dime and quarters totaled $5.25. How many quarters did she have? 8.) The Chans electric bill for September was $40.70, which included a tax of If Chans used 320 kwh of electricity that month, find the cost per kilowatt-hour. 9.) The sum of two numbers is -2. If twice the smaller numbers is added to three times the larger, the result is 1. Find the numbers. 10.) Helen has 2 more than twice as many stamps as Gail. If Gail buys 10 more stamps, she and Helen will have the same number of stamps. How many stamps does each person have now? 11.) The manager of Craft Shoppe bought some rug kits for $16 each, sold all but 6 of them for $22 each, and made profit of $168. How many kits were originally bought? 12.) The sum of 37 and three times a number is 67. Find the number. 13.) Four times a number, decreased by 24, is -20. Find the number.

3 14.) The perimeter of rectangle is 108. If the length is 33, find the width. 15.) A large bucket holds 3 L more than twice as much as a small bucket. It took 2 small buckets and 5 large buckets to fill a 63 L tank. How much does a large bucket hold? 16.) The lengths, in meters, of the sides of a triangle are consecutive even integers. The perimeter is 18 m. How long are the sides? 17.) Bruce s savings account contains $122 more than his younger brother s account. Together, they have $354. Find the amount in each account. 18.) Jay s salary is 2/3 of his wife s salary. In January, when they both get $2000 raises, their combined income will be $49,000. What are their current salaries? 19.) Erin s three test scores were consecutive odd integers. If her next test score is 18 points more than the highest score of the three tests, her total number of points will be 328. Find Erin test scores. 20.) Julius weighs twice as much as each of his twin brothers. If each of the twins gains 5 lb and Julius gains twice that amount, the sum of the three brothers weights will be 240 lb. How much does each weigh now? 21.) The width of rectangle is 6 cm less than the length. A second rectangle, with perimeter of 54 cm, is 3 cm wider and 2 cm shorter than the first. What are the dimensions of each rectangle?

4 22.) Martha has some nickels and dimes worth $6.25. She has three times as many nickels as dimes. How many nickels does she have? 23.) Elliot paid $1.50 a dozen for some flowers. He sold all but 5 dozen of them for $2 a dozen, making a profit of $18. How many dozen flowers did he buy? 24.) Rachel spent $16.18 for some cans of dog food costing 79 cents each and some cans of cat food costing 69 cents each. She bought two more cans of cat food than dog food. How many cans of each did she buy? 25.) Victor earns $3 an hour working after school and $4 an hour working on Saturdays. Last week he earned $43, working a total of 13 h. How many hours did he work on Saturday? 26.) A honeydew melon costs four times as much as a peach. Together they cost $1.50. How much does each cost? 27.) Find three consecutive integers whose sum is ) Thirty-eight employees at High Tech Sales ride to work on the subway. This represents 2/5 of the employees. How many employees are there? 29.) Rory has 30 coins (all nickels and dimes). He has five times as many nickels as dimes. How much money does he have? 30.) A number increased by 13 is -5. Find the number.

5 31.) A glass of milk costs 70 cents. If a glass of milk and a sandwich cost $2.50, how much does the sandwich cost? 32.) Fifteen less than a number is 43. Find the number. 33.) A plane flew 145 km/h faster when it was flying with the wind than it would have flown in still air. If its speed with the wind was 970 km/h, find the speed of the plane in still air. 34.) The Booster Club had $425 in its treasury. The members earned $642 selling refreshments. They denoted $320 to the football team for bus rentals. How much money did they have left? 35.) Seventy-six tickets were sold in advance for a museum field trip. Thirteen tickets were sold the day of the trip. Seven people had to return their tickets and did not go. How many people went together? 36.) The opposite of seven times a number is 238. Find the number. 37.) One fourth of a number is 73. Find the number. 38.) kg bag of apples costs $1.40. Find the cost per kilogram of the apples. 39.) Frank works the same number of hours each week at a part-time job. In the last 8 weeks he worked 68 h. How many hours does Frank work each week?

6 40.) A rectangle is 24 cm long and has a perimeter of 72 cm. Find the width. 41.) A restaurant cuts its large pizza into 8 slices and sells each slice for 90 cents. If the pizza were cut into 6 slices, how much would the restaurant have to charge for each slice to make the same amount? 42.) If you subtract 34 from the product of 15 and a number, you get 146. Find the number. 43.) The perimeter of rectangle is 120 cm. The width is 35 cm. Find the length. 44.) Charlene paid $131.44, including tax, for a desk. The tax was 31 cents less than 1/16 the cost of the desk. Find the cost of the desk. 45.) Twin Cinema I seats 150 more people than Twin Cinema II. If the cinemas seat 1250 people altogether, find the number of seats in Twin Cinema II. 46.) A bank contains 36 nickels, dimes and quarters. There are 4 more dimes than quarters and twice as many nickels as quarters. How many of each coin are in the bank? 47.) The longest side of a triangle is 8 cm longer than the shortest side and 5 cm longer than the third side. If the perimeter f the triangle is 56 cm, find the lengths of the three sides.

7 48.) The larger of two consecutive integers is 10 more than twice the smaller. Find the integers. 49.) Find a number whose product with 6 is the same as its sum with ) Five times a number, increased by 3, is the same as three times the number, increased by 27. Find the number. 51.) The sum of two numbers is 20. Twice one number is 4 more than four times the other. Find the numbers. 52.) The lengths of sides of a triangle are consecutive odd integers. If the perimeter is 1 less than four times the shortest side, find the length of each side. 53.) A sandwich costs 20 cents more than a salad plate. Six sandwiches cost as much as seven salad plates. Find the cost of each. 54.) Kevin works 3 times as many hours in a week as Karen does. If each were to work 6 h more per week, Kevin would be working twice as many hours as Karen does. How many hours does each work now? 55.) Aaron, Betsy and Charita work part-time at public library. Betsy works 4 h more each week than Aaron, and together they work half as many hours as Charita. How long does each person work if their total time is 48 h?

8 56.) Zach s last quiz score was 30 points less than twice his first score. What was his first quiz score if the sum of his two scores is 150? 57.) The length of a rectangle is 18 cm more than the width. A second rectangle is 6 cm shorter and 3 cm wider than the first and has a perimeter of 126 cm. Find the dimensions of each rectangle. 58.) Becky has as many dimes as Ryan and Amy have together. Ryan has 2 more dimes than Amy, and Amy has one third as many dimes as Becky has. How many dimes does each have? 59.) A cup of skim milk has 10 more than half the calories of a cup of whole milk. A cup of whole milk has 40 more calories than a glass of apple juice. If the total number of calories in one cup of each is 370, find the number of calories in each. 60.) A collection of quarters and dimes is worth $6.75. The number of dimes is 4 less than three times the number of quarters. How many of each are there? 61.) A total 720 people attended the school basketball game. Adult tickets cost $2.50 each and student tickets cost $1.50 each. If $1220 worth of tickets were sold, how many students and how many adults attended? 62.) A worker earns $9 per hour for a regular workday and $13.50 per hour for additional hours. If the worker was paid $ for an 11-hour workday, what is the length of a regular workday?

9 63.) Carrots cost 75 cents per kilogram and potatoes cost 70 cents per kilogram. A shopper bought 9 kg of the vegetables for $6.60. How many kilograms of each did the shopper buy? 64.) A collection of 102 nickels, dimes and quarters is worth $ There are 14 more nickels than dimes. How many quarters are there? 65.) The sum of twice a number and -6 is 9 more than the opposite of the number. Find the number. 66.) Roger spent $22 on a baseball mitt and softball. If the mitt cost $2 less than 5 times the cost of softball, find the cost of each. 67.) I drove 450 km in 6 h. Find my rate of travel. 68.) The longs checking account was overdrawn by $ They deposited $580 in the account. Then they wrote checks for $25 and $ Find their new balance. 69.) Alice bought 12 apples and oranges for $2.51. If an apple costs 25 cents and an orange costs 18 cents, how many of each did she buy? 70.) A rectangle has a perimeter of 48 cm. If the width and length are consecutive odd numbers, find the dimensions of the rectangle. 71.) The usual July temperature in Windsor, Ontario, 22 degrees, is 27 degrees above the usual January temperature. Find the usual January temperature.

10 72.) When 7 is decreased by a number, the result is 10. Find the number. 73.) Find three consecutive integers such that three times the smallest is equal to the middle number increased by the greatest number. 74.) What is the difference between the boiling point of mercury, 357 degrees, and the melting point, -39 degrees? 75.) Ruwa has $125 in $5 bills and $10 bills. If he has four more $5 bills than $10 bills, how many of each does he have? 76.) A store manager bought c calculators for $8 each. All but four were sold for $10 each. The remaining four calculators were not sold. Find the store s profit, in simplified form, in terms of c. 77.) At a city zoo, about $45 of every $100 spent is used for animal care and supplies. One year $216,000 was spent on these uses. Find the total zoo budget that year. 78.) Denise did 7/8 of the problems on a quiz correctly and five incorrectly. She did all the problems. How many were there? 79.) On Saturday Kim worked three hours more than Ann did. Together, they worked one hour less than three times the hours Ann worked. How many hours did Kim work?

11 80.) A bank contains 44 coins (nickels, dimes and quarters). There are twice as many dimes as nickels and 8 fewer nickels than quarters. How much money is the in the bank? 81.) Sara has twice as much money as Miguel. If he had $6 more, she would have 4/3as much money as he has. How much money does each have now?