2010 AMC 10B Problem 15

Question

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?

25

27

29

31

33

Let

R

be correct answers and

W

wrong answers

Use

4R-W=99

and

R+W\le50

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.

Problem 15 in other years