SAT Math Multiple Choice Question 265: Answer and Explanation

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Question: 265

10.

The figure above shows the rate at which a textile machine can produce a wool-polyester blend fabric. To produce a 100% polyester fabric, the same machine can produce 40 square yards per hour. Given that the company needs to fill an order for 2,400 square yards of each type of fabric, which of the following statements is true?

  • A. It will take half as long to make the blended fabric as the 100% polyester fabric.
  • B. It will take twice as long to make the blended fabric as the 100% polyester fabric.
  • C. It will take 20 more hours to make the blended fabric than the 100% polyester fabric.
  • D. It will take 20 fewer hours to make the blended fabric than the 100% polyester fabric.

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Start by finding the rate at which the blended fabric is produced according to the graph. To do this, find the slope by picking two points and using the formula Pay careful attention to how the grid-lines are labeled.

Getting to the Answer: Using the points (0, 0) and (2, 60), the slope is which means the machine produces 30 square yards of the blended fabric per hour. The question states that the machine can produce the 100% polyester fabric at a rate of 40 square yards per hour. Now, determine how long it would take the machine to produce 2,400 yards of each fabric:

Blended: 2,400 ÷ 30 = 80 hours

100% polyester: 2,400 ÷ 40 = 60 hours

This means it will take 20 more hours to make the blended fabric than the 100% polyester fabric, which matches (C).

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