Question

Your next math test is worth 144 points and contains 40 problems. True/Falsequestions are worth 2 points each and multiple choice questions are worth 4points each. How many of each question type are there?TAletta

Answer 1

Given that there are total of 144 points in the test and contains 40 problems.

The true/false questions are worth 2 points each and multiple-choice questions are worth 4 points each.

We have to find the number of each type of question.

Let the number of true/false questions be x and the number of MCQ be y.

So,

$x+y=40$

and

$2x+4y=144$

From the first equation, we have y = 40 - x. Put this value in the second equation

$\begin{gathered} 2x+4(40-x)=144 \\ 2x+160-4x=144 \\ -2x=144-160 \\ -2x=-16 \\ x=\frac{-16}{-2} \\ x=8 \end{gathered}$

We have x = 8. Put x = 8 in y = 40 - x.

$\begin{gathered} y=40-8 \\ y=32 \end{gathered}$

Thus, there are 8 true/false questions and 32 MCQ in the test.