Chapter 6.3, Problem 17P

Your math test has 38 questions and is worth 200 points. The test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. How many of each type of question are there?

To determine

To calculate:Type of questionswas in the math’s test.

Answer to Problem 17P

4 points questions =35 and,

20 points question = 3.

Explanation of Solution

Given information:

Total number of questions = 38.

Total points = 200.

Question consist of 4 points and 20 points.

Calculation:

Let’s us consider that

4 points questions = X and

20 points question = Y

Therefore, according to question,

  $\begin{array}{l}X+Y=38\text{}\mathrm{.....}(i)\\ 4X+20Y=\mathrm{200.....}(ii)\end{array}$

Solving equation (i) we get-

  $X=38-Y$

Putting the value of X in equation (ii) we get-

  $\begin{array}{l}4X+20Y=200\\ 4\left(38-Y\right)+20Y=200\\ 152-4Y+20Y=200\\ 16Y=200-152\\ 16Y=48\\ Y=\frac{48}{16}=3\end{array}$

Therefore,

  $Y=3$ ,20 points question

Now putting the value of Y in equation (i) we get-

  $\begin{array}{l}X+3=38\\ X=38-3\end{array}$

  $X=35$ , 4 points questions

So,

4 points questions =35 and,

20 points question = 3.