Question

A 35 question test contains both multiple choice and true/false questions. the true/false questions are worth two points each and the multiple choice questions are worth three points each. if the test has a total of 100 possible points, how many of each type of question is on the test?

Answer 1

To find the number of true/false and multiple choice questions on the test, we can use a system of equations. By solving the equations, we find that there are 5 true/false questions and 30 multiple choice questions on the test.

Step-by-step explanation:

To solve this problem, let's use a system of equations:

Let T be the number of true/false questions and M be the number of multiple choice questions.

We know that each true/false question is worth 2 points and each multiple choice question is worth 3 points.

So we can create the following equations:

T + M = 35

2T + 3M = 100

By solving these equations, we can find the values of T and M:

Multiply the first equation by 2:

2T + 2M = 70

Subtract the second equation from the modified first equation:

(2T + 2M) - (2T + 3M) = 70 - 100

-M = -30

M = 30

Substitute the value of M into the first equation:

T + 30 = 35

T = 35 - 30

T = 5

Therefore, there are 5 true/false questions and 30 multiple choice questions on the test.