Question

Your class will be participating in a quiz show. Each multiple choice question isworth 5 points while each open-ended question is 15 points. The team needs toget 40 questions correct for a total of 350 points. How many of each questionmust be answered?

Answer 1

Let x be the number of 5 point questions and y be the number of 15 point questions.

So we have,

5x+15y = 350 ....... (1)

Also, x + y = 40

So,

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

Substituting the value of x in first equation,

$\begin{gathered} 5(40-y)+15y=350 \\ 200-5y+15y=350 \\ 10y=150 \\ y=15 \end{gathered}$

Therefore,

$x=40-15=25$

Thus, there are 25 questions of 5 points and 15 questions of 15 points.