Expert: Scott A Wilson - 12/7/2010

Question
I am having a difficult time solving this problem in my pre-calc class could you please help me.

Question: The pre-calc quiz consists of computation problem and graphing problems. Computation problems are worth 6 points each and graphing are worth 10 points each. You can answer a computation problem in 2 minutes and a graphing problem in 4 minutes. You have forty minutes to take the quiz and may choose no more than 12 problems to answer. Assuming you answer all the problems correctly, how many of each type should you answer to get the highest score.  

Answer
The 6 point problems take 2 minutes, so that is 3 points per minute.
The 10 point problems take 4 minutes, so that is only 2.5 per minute.

This would lead to answering as many 2 point questions as possible.

However, there is a 12 question limit, so lets answer x 6 pointers and 12-x 10 pointers.  Total time would be 2x + 4(12-x) = 48 - 2x.

Given there is 40 minutes for the test, set 48 - 2x = 40 and solve for x.  Thus, you wil answer x 6 point problems and 12-x 10 point problems.