Question

5. Your teacher is giving a test worth 100 points. The test contains a total of 40questions. Some questions are worth 2 points and some questions are worth 4points on the test. How many of each type of question are on the test? 30 twopoint questions and 10 four point questions.

Answer 1

Given:

Total points =100

Let, x= number of 2 point questions.

y= number of 4 point questions.

There are 40 questions

This we can write,

$x+y=40\ldots\text{.}(1)$

Since, the test is worth 100 points. this can be written as,

$2x+4y=100\ldots\text{.}\mathrm{}(2)$

Equation (1) can be written as,

$x=40-y$

Put the value of x in the equation (2),

$\begin{gathered} 2(40-y)+4y=100 \\ 80-2y+4y=100 \\ 2y=100-80 \\ y=\frac{20}{2} \\ y=10 \end{gathered}$

Now put the value of y in equation (1),

$\begin{gathered} x+y=40 \\ x+10=40 \\ x=30 \end{gathered}$

So, the number of 2 point questions are x=30

and number of 4 point questions are y=10