Question

Ms. Rodriguez gave a test that had 42 questions consisting of Multiple Choice and short answer questions. If the test is worth 60 points and Multiple Choice questions are worth 1 point and short answer questions are worth 3 points, how many Multiple Choice & Short Answer questions were on the test that Ms. Rodriguez gave?

Answer 1

There are 33 multiple choice questions and 9 short answer questions on the test

Explanation:

In this question, we are asked to calculate the number of multiple text answers and short answers given in a test, given that the test taker will attempt a number of questions and have a particular score.

Since we do not know the number of these questions individually, let’s represent them with variables. Let the number of multiple choice questions to be answered be x and the number of short answers questions to be given be y.

Mathematically,

x + y = 42. (I)

Also, the total points is 60, with multiple choice of 1 point each and short answers of 3 points each. Mathematically, this means;

x(1) + y(3) = 60.

x + 3y = 60. (ii)

Now let’s solve both 1 and 2 simultaneously.

From 1, let’s say y = 42-x and substitute this in 2

x +3(42-x) = 60

x + 126 -3x = 60

-2x = 60-126

2x = 66

x = 66/2

x = 33

From y = 42-x, we can substitute the value of x and get y.

y = 42-33

y = 9