Question

A test worth 125 points has 49 questions on it. Multiple Choice questions are worth 2 points each and short answer questions are worth 5 points each. How many of each type of question are on the test?

Answer 1

There were 40 2-point questions and 9 3-point questions.

Explanation:

To solve this situation, write two equations. One for the number of questions and one for the number of points.

Let x be the number of 2 point questions.

Let y be the number of 5 point questions.

x + y = 49

Now since x are each worth 2 points, the total points is 2x.

And since y are each worth 5 points, the total points is 5y.

So 2x + 5y = 125. Substitute one of the equations into the other to solve for the variables.

x + y = 49 becomes x = 49 - y. Substitute it.

2(49-y) + 5y = 125

98 - 2y + 5y = 125

98 + 3y = 125

3y = 27

y = 9

Substitute y = 9 back into the equation x = 49 - y to find x.

x = 49 - 9

x = 40