Question

a test is worth 80 points.multiple choice questions are worth 2 points,and short-answer questions are worth 4 points.if the test has 25 questions,how many multiple-choice questions are there?

Answer 1

Let
`x` be the number of multiple choice questions and
`y` the number of short-answer questions.

Now,


`\begin{cases}x+y=25\\2x+4y=80\end{cases}`

Since you only care about finding
`y`, you can substitute the first equation into the second to eliminate
`x`. You have


`x+y=25\implies x=25-y`

and substituting into the other equation,


`2(25-y)+4y=80`

`50-2y+4y=80`

`2y=30`

`y=15`