CLASSWORK PROBLEMS

WORD PROBLEMS

DIRECTIONS:

  • Write money in proper form.
  • Reduce fractions/ratios to lowest terms.
  • Round decimals to nearest cent/hundredth.

DO NOT USE A CALCULATOR!!!

Translate each sentence and then simplify the expression.

1) Add twice the quantity 3x + 5 from the quantity 4x -7.

2) Subtract four times the quantity 2x + 3 from twice the quantity 6x - 11.

3) Subtract three times the quantity 2x - 5 from five times the quantity 4x + 7.

4) Multiply the quantity 3x2– 5x - 7 by (-1) and add that product to the quantity 14x2– 11x + 24.

Write an equation and then solve.

5) Twice the sum of a number and six is ten less than the number. What is the number?

6) The center of an NFL football team weighed 137 pounds more than his wife. If their total weight was 395 pounds, then how much does each person weigh?

7) The sum of three consecutive whole numbers is 306. Find the numbers.

8) Find the three consecutive odd integers in which the sum of the smallest and largest integer is the product of two and seven.

9) Kay is 15 years older than Sue. In six years, Kay will be twice as old as Sue. How old are they now?

10) An owner of a pizza shop spends $600 a month on rent. If this is 30% of his sales, find the sales for the month.

11) A tanning salon owner spends 4.7% of her sales on advertising. If sales for the month were $4568, find the amount spent on advertising.

12) A manager was given the challenge to increase sales from $450,000 to $635,000 per month. Find the percent increase of sales.

13) A certain hotel claims that it keeps 12.5% of its rooms for smokers. If the hotel has 680 rooms, how many rooms are for non-smokers?

14) It takes 3 hours to drive 210 miles. How many hours will it take to drive 1260 miles?

15) In a Brides magazine article, four out of seven men say they remember their wedding anniversary. If 63,000 men in New Jersey are surveyed, how many men would remember their anniversary?

16) In a survey, three out of every five eighth-graders smoke. If 240,000 eighth-graders were surveyed in New Jersey, how many of them do not smoke?

17) Forty-two pounds of fertilizer costs $12.50. At that rate, how much will it cost for ten pounds of fertilizer?

18) In a triangle, one angle is three times as large as the smallest angle. The third angle is 40 degrees greater than the smallest angle. Find the measurement of all three angles.

19) The length of a rectangle is 5 cm less than three times its width. If the perimeter of the rectangle is 54 cm, find the length and width of the rectangle.

20) If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a rectangle is formed whose perimeter is 40 cm. Find the length and width.

21) Leeza can paint the kitchen in 5 hours. Susan can paint the kitchen in 3 hours. If they work together, how long will it take to paint the kitchen?

22) An Olympic size pool can be filled by pipe A in 18 hours and by pipe B in 12 hours. There is also a drainpipe that can drain the entire pool in 8 hours. If the valves of both pipes are open and the drainpipe is also open, how long will it take to fill the pool?

23) Herman can build a cabinet in 8 hours. However, together Herman and Joshua can build the cabinet in 51/2 hours. How many hours would it take only Joshua to build the cabinet?

24) Theatre tickets sell $7.50 for adults and $5.00 for children. On Saturday, 100 more adult tickets were sold than children tickets. The total revenue was $3250. Find how many adult and children’s tickets were sold.

25) Seth has a bag with 30 quarters and dimes. The bag of coins is worth $5.70. Find how many of each coin is in the bag.

26) Jamilah has a bag of dimes and nickels worth $6.25. There are 5 more nickels than dimes. How many of each coin are there in the bag?

27) Roger and Patrick leave Giants Stadium at 11:00 PM going in opposite directions. Roger, the calm friend, drives 55 mph on Rt. 3 East and Patrick, the adventurous friend, drives 70 mph on Rt. 3 West. In how many hours will the two friends be 120 miles apart?

28) At noon a cargo plane leaves McHareAirport and heads east at 180 mi/h. At 1:00 PM a jet takes off from McHare and flies east after the cargo plane at 450 mi/h. At what time will the jet overtake the cargo plane?

29) Three times the greatest of three consecutive even integers exceeds twice the least by 38. Find the integers.

30) The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers.

31) One fifth of a number plus five times that number is equal to seven times the number less 18. Find the number.

32) Find three consecutive integers whose sum is -33.

33) Find two consecutive odd integers whose sum is 196.

34) Twelve decreased by twice a number is -7. Find the number.

35) Find four consecutive integers whose sum is 86.

36) Willie’s weight is 2 pounds less that twice his son’s weight. Willie weighs 174 pounds. Find Willie’s son’s weight.

37) Five years ago, John’s age was half of the age he will be in 8 years. How old is he now?

38) John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be three times as old as Alice. How old is Peter now?

39) John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

40) Jane bought a pencil and received change for $6 in 20 coins, all nickels and quarters. How many of each kind are given?

41) John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?

42) The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

43) The sum of the least and greatest of 3 consecutive integers is 60. What are the values of the 3 integers?

44) The lengths of the sides of a triangle are consecutive odd numbers. What is the length of the longest side if the perimeter is 45?

45) John has a board that is 5 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be in inches?

46) Jane and her friends were selling cookies. They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week. Altogether, they sold a total of 352 boxes. How many boxes did they sell in the third week?

47) Bob's father is 3 times old as Bob. 4 years ago, he was 4 times older. How old is Bob?

48) In January of the year 2000, my husband John was eleven times as old as my son William. In January of 2012, he will be three times as old as my son. How old was my son in January of 2000?

49) In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?

50) One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

51) Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone dollar coins. The twenty-six coins in his pocket are dollars and quarters, and they add up to seventeen dollars. How many of each coin does he have?

52) A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?

54) A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?

55) Twice the larger of two numbers is three more than five times the smaller, and the sum of four times the larger and three times the smaller is 71. What are the numbers?

56) Karen is twice as old as Lori. Three years from now, the sum of their ages will be 42. How old is Karen?

57) Tony has 11 more nickels than quarters. How many coins does he have if the total value of his coins is $2.65?

58) You have $50,000 to invest, and two funds that you'd like to invest in. The You-Risk-It Fund (Fund Y) yields 14% interest. The Extra-Dull Fund (Fund X) yields 6% interest. Because of college financial-aid implications, you don't think you can afford to earn more than $4,500 in interest income this year. How much should you put in each fund?"

59) An investment of $3,000 is made at an annual simple interest rate of 5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total annual interest earned is 7.5% of the total investment?