2014-07-07 09:00:42

Giancarlo spent three weeks working on a project for his science class. During the second week, he worked 1 2/3 times the number of hours he worked during the first week. During the third week, he worked twice the number of hours he worked during the second week. If he worked an average of 12 hours per week during the three weeks, how many hours did Giancarlo work the third week?

(A) 6
(B) 10
(C) 16
(D) 20
(E) 24

The correct answer is D
Explanation: Start with the most specific piece of information. Here, that is the fact that he worked an average of 12 hours a week, which means he worked a total of 36 hours over the three weeks (since 12 x 3 is 36).

Now, set up an equation using x for the number of hours he worked week 1. If he worked x hours week 1, he would've worked 5/3 times x hours the second week, and 10/3 times x hours the third week. These weeks would have to sum to 36. Thus,

x + (5/3)x + (10/3)x = 36.

Simplify to get 6x = 36. Solve for x by dividing both sides by 6 to get x = 6.

This means that Giancarlo worked 6 hours the first week. The question asks for the number of hours he worked the third week, which would be 10/3 times 6, or 20 hours. Thus, choice D is correct.