MCAS 2001, 8th Grade Math, Questions 37 to 39

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Question #37

Which of the following describes one way to solve this equation?

12 - 3x = 5

A. Add 3x to both sides, then divide both sides by 3.

B. Subtract 3x from both sides, then multiply both sides by 3.

C. Add 12 to both sides, then multiply both sides by -3.

D. Subtract 12 from both sides, then divide both sides by -3.

Question #38

Ms. McCarthy's class is making up number puzzles. These are two of the puzzles.

Haan's puzzle:

My number is the product of three different prime numbers.
It is an odd number less than 125.
The sum of its digits is a multiple of 3.
One of its factors is the third prime number.
What is my number?

Manuel's puzzle:

My number is even.
It is a factor of 198 and a multiple of 9.
It is less than 100.
What is my number?

a. What is Manuel's number?

b. What is Haan's number? Explain the strategy you used to find your answer to Haan's puzzle.

c. Write a number puzzle that

has exactly three clues,
has one and only one answer, and
includes the following words: factor and prime number.

Question #39

Some eighth-grade students want to raise at least $300 for a field trip by selling popcorn and fruit bars. The chart below shows the amount of profit they will make on each sale.

a. If they sell exactly 500 fruit bars, how many boxes of popcorn will they need to sell to make a total of $300?

b. On the grid in your Student Answer Booklet, draw a graph showing the combinations of boxes of popcorn and fruit bars they must sell to make a total of exactly $300. Let the horizontal axis represent the number of fruit bars. Label that axis to 1,000. Show or describe the calculations you used to find the data points for your graph.

c. Based on last year's sales, the students will probably not be able to sell more than 600 fruit bars. Using your graph, explain how you can find the number of boxes of popcorn the students must sell to make a total of $300 if they sell exactly 600 fruit bars. How many boxes of popcorn must they sell?

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