Question

Your next Pre-Algebra test is worth 93 points and contains 38 multiple choice and short answer problems. Each

multiple choice problem is worth two points and each short answer is worth three points. How many of each type of
problem is on the test?

Answer 1

There are 21 multiple-choice problems and 17 short answers.

Explanation:

Let there are x multiple-choice problems and y short answers.

ATQ,

x+y = 38 ....(1)

Each a multiple-choice problem is worth two points and each short answer is worth three points.

2x+3y = 93 ....(2)

Multiply equation (1) by 2.

2x+2y = 76 ....(3)

Subtract equation (2) and (3) we get :

2x+3y-(2x+2y) = 93-76

2x+3y-2x-2y = 17

y=17

Put the value of y in equation (1).

x+17 = 38

x=21

Hence, there are 21 multiple-choice problems and 17 short answers