Math 8 Levels II & III. For each problem, write a let statement, write and solve an equation, and answer the question.

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Math 8 Levels II & III Word Problems Name Date Section For each problem, write a let statement, write and solve an equation, and answer the question. Integers: 1.

Find the number. 4. If twice a number is decreased by 10, the result is 16. Find the number. 5. The larger of two numbers is 4 times the smaller.

1 Math 8 Levels II & III Word Problems Name Date Section For each problem, write a let statement, write and solve an equation, and answer the question. Integers: 1. When twice a number is increased by 3, the result is 29. What is the number? 2. Six less than twice a number is -14. Find the number. 3. One more than two-thirds of a number is nineteen. Find the number. 4. If twice a number is decreased by 10, the result is 16. Find the number. 5. The larger of two numbers is 4 times the smaller. If the larger number exceeds the smaller number by 15, find the numbers. 6. In his will, Uncle Al left $5000 to his two nieces. Emma s share is to be $500 more than Alice s because he liked her better. How much will each niece receive? 7. Eight times a number equals 35 more than the number. Find the number. 8. The second of three numbers is six more than the first. The third number is twice the first. The sum of the three numbers is 26. Find the three numbers. 9. The sum of two consecutive integers is 17. What are the integers? 10. The sum of two consecutive integers is -9. Find the integers. 11. The sum of two consecutive even integers is -34. Find the integers. 12. The sum of three consecutive even integers is 48. Find them. 13. The sum of three consecutive integers is 39. Find the integers. 14. The sum of four consecutive integers is -46. Find the integers. 15. The sum of two consecutive odd integers is 36. Find them. 16. The sum of three consecutive odd integers is -75. What are they? 17. Find three consecutive odd integers whose sum is Find three consecutive integers whose sum is Find three consecutive odd integers such that the smallest plus twice the middle is thirty less than five times the largest One number is 8 more than another. Their sum is -12. Find the numbers.

2 21. The greater of two number is 6 times the lesser. The greater is 25 more than the lesser. Find the numbers. 22. The greater of two numbers is 13 more than 2 times the lesser. Nine times the greater number is 5 more than 4 times the lesser. Find the numbers. 23. The greater of two numbers is 7 more than the lesser. Three times the greater number is 5 more than 4 times the lesser number. Find the numbers. 24. If 7 times a number is decreased by 33, the result is 15 less then 10 times the number. Find the number. 25. When two times a number is increased by 10, the result is 1 more than 3 times the number. Find the number. 26. The greater of two numbers is twice the lesser. If the greater is increased by 18, the result is 4 less than 4 times the lesser. Find the numbers. 27. If a number is doubled and then increased by 20, the result is 5 less than 3 times the number. Find the number. 28. The sum of three numbers is 123. The second number is 9 less than two times the first number. The third number is six more than three times the first number. Find the numbers. General Word Problems: 29. Mike wants to buy a new bike. That costs $ That is $24.00 more than 3 times what she saved last month. How much did she save last month? 30. One season, Pete Rose scored three fewer runs than twice the number of runs he batted in. He scored 103 runs that season. How many runs did he bat in? 31. You have a 90 pound calf that you expect to gain 65 pounds per month. How long will it take for the calf to reach 1000 pounds? 32. Bill Dupp s Lumber Yard charges $.50 for each cubic foot of sand plus $16.00 to deliver. The number of dollars that you will pay is 0.50 times the number of cubic feet you order plus 16 delivery charge. How much sand would you get delivered if your bill was $ When the meter on a taxi is first turned on it reads $3.75. As the taxi travels $2.25 is added for each quarter of a mile driven. If your fare was $24.00, how far did you ride? 34. Pete s Plumbing charges $95.00 for a service charge plus $82.00 per each additional hour he works on your home. If you receive a bill for $464.00, how long was he working in your home? 35. The bill for the parts and labor to repair your car is $ The parts totaled $ and labor is $34 per hour. How many hours did they charge you for labor? 36. Phil T. Rich has $6000 and is spending $150 per week. Lotta Spences only has $2500, but she is saving $250 per week. After how long will they have the same amount of money?

3 37. Moe Tell has $300 to spend on holiday presents and is adding to that amount at a rate of $5 per day. Fran Tick has $420 but is spending $7 per day. After how many days will they have the same amount of money? 38. The temperature in Hawaii is 96 degrees, but is dropping at a rate of 4 degrees per hour. In San Jose it is 72 degrees but it is rising 2 degrees per hour. In how many hours will it be the same temperature? 39. Kay Oss weighs 187 pounds but is on a diet where she loses 1.7 pounds per week. Dan D. Lyons is only 93 pounds but wants to gain weight for wrestling season so he is on a diet that allows him to gain 0.9 pounds per week. After how many weeks will they weigh the same amount? 40. One telephone company charges $16.95 per month plus 5 cents per minute for local calls. Another phone company charges $22.95 per minute, but only 2 cents per minute for local calls. After how many minutes of local calls will the two calling plans be the same? 41. One health club charges $99 to join plus $79 per month. Another club charges $159 to join but only $64 per month. After how may months is the cost the same? 42. A rock climbing gym charges nonmembers $16 per day to use the gym and $8 per day for equipment rental. Members pay a yearly fee of $450 for unlimited climbing and $6 per day for equipment rental. How many times must you use the gym to justify membership? 43. A team scored a total of 22 runs in three games. In the first game, they scored twice as many runs as in the second game. In the second game, they scored two less runs than in the third game. How many runs did the team score in each? 44. A movie theater collected $1000 in admission fees for a particular showing. There are 20 more adults than children. An adult ticket costs $10 and a child ticket costs $6. How many adults and how many children attended the movie? Money: 45. A wallet contains only $5-bills and $10-bills. There are 8 more $5-bills than $10-bills and the wallet contains $220. How many of each bill are in the wallet? 46. A purse contains only quarters and dimes totaling $4.35. If there are 30 coins in all, how many of each type of coin is in the purse? 47. Mr. Block has $10 consisting of quarters, dimes and nickels. If he has 10 more dimes than quarters and twice as many nickels as quarters, how many of each coin does he have? 48. Lana collects quarters and dimes. The number of dimes in her collection is three times the number of quarters. If the number of dimes exceeds the number of quarters by eight, what is the value of Lana s coin collection? 49. Catherine purchased 15 stamps at the local Post Office valued at 37 and 39 cents. She paid with a $10-bill and received $4.35 change. How many 39 cent stamps did she buy? Geometry: 50. The width of a rectangle is seven less than its length. If the perimeter is 70 inches. what is the length and width of that rectangle?

4 51. The perimeter of a rectangle is 48 cm. If the length of the rectangle is 16 cm, then what is the width? 52. The length of a rectangle is three more than twice its width. If the perimeter is 126 yards, what is the length and width? 53. The sides of a triangle are represented by x - 2, x + 11, and 2x + 3. If the perimeter of the triangle is 50 cm, what is the length of each side? 54. A garden is in the shape of an isosceles triangle. The length of the third side is two feet longer than the lengths of the two equal sides. If the perimeter of the garden is 86 feet, find the length of each side of the garden. 55. In an isosceles triangle, one side is two less than half the measure of the other two sides. If the perimeter of the triangle is 48, what is the measure of each side? 56. The perimeter of a rectangle is 52 feet. The length is two feet more than 5 times the width. Find the dimensions of the rectangle. 57. A rectangle has a perimeter of 225 in. The length is three and one-half times the width. Find the length and width. 58. The length of each side of an equilateral triangle is 5 cm more than the length of each side of a square. The perimeters of the two figures are equal. Find the lengths of the sides of the square and of the triangle. 59. The length of each side of a regular hexagon is 4 inches less than the length of the side of a square. The perimeter of the hexagon is equal to the perimeter of the square. Find the length of the side of the hexagon and a side of the square. Word Problems Involving Proportion & Percent Example: Naturalists have observed that there are 3000 fish in Lake Muchimuck. Some are perch and some are bass. When they drag a net through the lake they catch 24 perch and 21 bass. What is the ratio of perch to bass expressed in lowest terms? number of perch 24 = 8 number of bass 21 7 Assuming that the entire lake has this ratio, how many of each kind of fish are there? Let x = the common factor 8x = number of perch 7x = number of bass Write an equation: 8x + 7x = 3000 Solve the equation: x = 200 Answer the question: There are 1600 perch and 1400 bass in the lake 60. The ratio of two integers is 13 : 6. The smaller integer is 54. Find the larger integer. 61. The ratio of two integers is 7 : 11. The larger integer is 187. Find the smaller integer.

5 62. Mae Berry has 18 granddaughters and 12 grandsons. What is the ratio of these numbers in lowest terms? She plans to leave 7200 acres of land in two tracts whose areas are in this ratio. How many acres are in each tract? 63. You are an intern for the New York Knicks and they are planning a give-away for women only. There are 12,000 people at tonight s game and from a small sample you find the ratio of men to women is 3 : 2. About how many give-away items should you plan to have? 64. A large jar contains 8400 nuts. You will win the jar if you guess closest to the number of peanuts in the jar. You examine that jar and determine the ratio of peanuts to other nuts is 3 : 4. Based on this information, what will you guess is the number of peanuts? 65. You work in the dairy department at Stop & Shop where there is enough space to stock 320 one-gallon containers of milk. Sales figures show that the Stop & Shop brand milk outsells the national brand by 7 : 3. How many containers of each kind should you put in the case to maintain this ratio? 66. The local gas station finds sells regular, unleaded, and premium-unleaded gas in the ratio of 5 : 7.: 2 The station is delivered 35,000 gallons of gas per month. How many gallons of each type of gas should they order to maintain their sales ratio? 67. The sides of a triangle are in the ratio of 7 : 10 : 11. The perimeter is 112 inches. How long is each side? 68. The sides of a triangle are in the ratio of 6 : 7 : 10. The perimeter is 184 cm. How long is each side? 69. The length and width of a rectangle are in the ratio of 3 : 2. The perimeter is 73 inches. Find the length and width. 70. Ecologists are trying to determine how many fish there are in a particular lake. They catch and tag 100 fish and return them to the lake. Several days later they catch 15 fish and find that only two are tagged. What is the ratio of tagged fish to untagged fish? How many Assuming this ratio, how many fish are in the lake? 71. The measures of the angles of a triangle are in the ratio 2 : 2 : 5. What is the measure of each angle? *72. Ike has 50 more marbles than one-third of what Jack has. If the ratio of the number of marbles that Ike has to the number that Jack has is 2 : 3, how many marbles does each of them have? 73. The denominator of a fraction is 11 more than the numerator of the fraction. The value of the fraction is 2 / 3. Find the fraction. 74. The numerator of a fraction is 9 less than 3 times the denominator. The value of the fraction is 5 / 2. Find the fraction 75. The numerator of a fraction is 6 less than the denominator. If the numerator is multiplied by 2 and the denominator remains unchanged, the resulting fraction is equivalent to ½. Find the original fraction.

6 76. The numerator of a fraction is three times the denominator. If the numerator is decreased by one and the denominator is increased by two, the value of the resulting fraction is 5 / 2. Find the original fraction. **Mixture: Example: Carbon monoxide is a gas that is 43% carbon. Carbon dioxide is only 27% carbon. The Environmental Protection Agency (EPA) analyzes exhaust from cars which is a mixture of carbon monoxide and carbon dioxide. They find a 1600 mg sample of exhaust gas with 32% carbon. How many mg of the sample were carbon monoxide and how many were carbon dioxide? x = number of mg of carbon monoxide x = number of mg of carbon dioxide 0.43x (1600 x) = 0.32(1600) Solve to find x = 500, so 500 mg of carbon monoxide and 1100 mg of carbon dioxide 77. Old silver coins contain 90% silver. Solver solder contains 63% silver. If you want to make 200 kilograms of alloy containing 82% silver, how many kilograms of old coins and silver solder should you melt together? fl. oz. of a 2% alcohol solution was mixed with 11 fl. oz. of a 66% alcohol solution. Find the concentration of a new mixture lbs. of mixed nuts containing 55% peanuts were mixed with 6 lbs. of another kind of mixed nuts that contain 40% peanuts. What percent of the new mixture is peanuts? gallons of a sugar solution was mixed with 6 gallons of a 90% sugar solution to make a 84% sugar solution. Find the percent concentration of the first solution. 81. How much soil containing 45% sand do you need to add to 1 ft 3 of soil containing 15% sand in order to make a soil containing 35% sand?

Name: Date: Algebra X-Box Word Problems. Name: Teacher: Pd:

Name: Date: Algebra X-Box Word Problems. Name: Teacher: Pd: Name: Date: Algebra 2011-2012 X-Box Word Problems Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Solve Word Problems by Converting into an Algebraic Equation. Pgs:1-5 HW: Pgs:6-8 DAY 2: SWBAT: Solve