2010 AMC 10B Problem 15

Problem 15 of 25IntermediateAlgebra

On a

50

-question multiple choice math contest, students receive

4

points for a correct answer,

0

points for an answer left blank, and

-1

point for an incorrect answer. Jesse’s total score on the contest was

99.

What is the maximum number of questions that Jesse could have answered correctly?

Show solution

Solution

Let

x

be the number of questions Jesse answered correctly and

y

be the number he answered incorrectly. Then

4x-y=99

and

x+y\leq50.

We have that

y = 4x - 99

5x - 99 \leq 50.

Rearranging and simplifying tells us that

x \leq 29.8.

Since

x

is an integer, its maximum value is

29.

Thus, C is the correct answer.