# Math Help - Word problem

1. ## Word problem

From a prealgebra problem book:

30% of the students in the Math Club are in the Science Club, and 80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club. How many students are in the Math Club?

I'm getting confused about what my variables and equations should be. Could anyone help out?

2. ## Re: Word problem

It's a good idea to start with what you can do.

'80% of the students in the Science Club are in the Math Club. There are 15 students in the Science Club'.

You can find out how many students in the Science club are also in the Math club.

15 x 0.8...

What can you do next?

3. ## Re: Word problem

Hello, Ragnarok!

30% of the students in the Math Club are in the Science Club,
and 80% of the students in the Science Club are in the Math Club.
There are 15 students in the Science Club.
How many students are in the Math Club?

Let $M$ = number of students in the Math Club.
Let $S$ = number of students in the Science Club.

$\begin{array}{cccc}\text{30\% of the Math Club is in both clubs:}& 0.30M \,=\,\text{both} \\\text{80\% of the Science Club is in both clubs:}& 0.80S \,=\,\text{both}\end{array}$

$\text{These quantities are equal: }\:0.30M \,=\,0.8S \quad\Rightarrow\quad M \,=\,\tfrac{8}{3}S$

We are told that: . $S \,=\,15$

Therefore . . .

4. ## Re: Word problem

Thank you so much! I was totally overlooking the fact that the numbers are equal. There are 40 students. : )

5. ## Re: Word problem

step 1-80% of 15=12
step2-now take 30% of a number, let say,x, i.e-30% of x =12
step 3- 12*100/30=40 (answer)