# A test is worth 50 points. Multiple choice questions are worth 1 point and short answer questions are worth 3 points. If the test has 20 questions, how many multiple choice questions are there?

May 10, 2018

There are 5 multiple choice questions.

#### Explanation:

Test=50 points
Multiple choice question= 1 point
There are 20 questions

I solved this by multiplying the question numbers by 3.

If there were 18 short answer questions, then you would solve

$18 \times 3 = 54$ points

Too much, considering the test is 50 points.

How about 17xx3?

That equals $51$, again, too much.

16xx3?

Equals $48$. This would seem like the perfect answer, except there are $16$ short answer questions, and to get to $50$ points we would only need $2$ multiple choice questions. That doesn't work, because this test has $20$ questions and we would only have $18 q u e s t i o n s$.

$15 \times 3 = 45$. This answer is perfect, because there are $15$ short answer questions, which totals to $45$ points. Now to make it to $50$ points, we only need $5$ more questions.

$15 + 5 = 20$

There are $15$ short answer questions and $5$ multiple choice questions. Wow, that's a hard test.