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?

$25$

$27$

$29$

$31$

$33$

Answer: C

Concepts:linear equation inequality optimization

Difficulty rating: 1420

Solution:

Let $x$ be the number of questions Jesse answered correctly and $y$ be the number he answered incorrectly.

Then $4x - y = 99 \text{ and } x + y \leq 50.$

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.

2010 AMC 10B Problem 15

Answer: C

Difficulty rating: 1420

Solution:

Problem 15 in Other Years