Question

There are 52 questions on Allison's English test. The multiple choice questions are worth 2 points each, and the short answer questions are worth 5 points each. The entire test is worth 155 points.

Let x = multiple choice questions, and y = short answer questions.

How many short answer questions are on the test?

Answer 1

this is going to be a system of equations problem. so we need to set up some equations. we know the test has 52 questions, and is made up of multiple-choice and short answer questions.

so x + y = 52 is our first equation

we know the entire test has 155 points, and the multiple-choice are 2 points, and the short answer are 5 points.

so 2x + 5y = 155 is our second equation

so our system of equations is

x + y = 52
2x + 5y = 155

Answer 2

there are a few ways to solve it. i think i'd use the substitution method. what do you think?