PSAT Math Multiple-Choice Question 620: Answer and Explanation

Question: 620

Rosa's metabolism is 65 calories per hour when resting and 300 calories per hour when exercising. If Rosa wants to burn more than 2,000 calories per day, what is the range of hours, H, she should spend exercising, ­calculated to the nearest tenth, assuming that she is either resting or exercising at any time in a given day?

• A. 24 > H > 1.9
• B. 24 > H > 2.4
• C. 24 > H > 6.7
• D. 24 > H > 22.1

Correct Answer: A

Explanation:

(A) Let's first set up an inequality that models this situation. Rosa wants to burn more than 2,000 calories, so we can represent this as 2,000 < calories.

Next we need to come up with an expression that represents the number of calories Rosa burns. Rosa is either burning 65 calories per hour by resting or burning 300 calories per hour while exercising. Let's call H the number of hours she spends exercising. Since there are 24 hours in a day and she's not exercising for the rest of the hours outside of H, the hours spent resting will be 24 - H.

Therefore, the number of calories Rosa burns can be expressed as:

2,000 < 300H + 65(24 - H)

Now we solve for H. First, distribute the 65:

2,000 < 300H + 1560 - 65H

Combine like terms:

2,000 < 235H + 1560

Subtract 1,560 from both sides:

440 < 235H

Divide both sides by 235:

1.87 < H

This means that Rosa has to work out for at least 1.9 hours. She can't work out more than 24 hours per day since there are only 24 hours in a day. So the correct answer is (A).