# Word problem

• Jul 8th 2012, 01:35 PM
Ragnarok
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?
• Jul 8th 2012, 02:12 PM
Furyan
Re: Word problem

'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?
• Jul 8th 2012, 02:35 PM
Soroban
Re: Word problem
Hello, Ragnarok!

Quote:

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 . . .

• Jul 8th 2012, 02:59 PM
Ragnarok
Re: Word problem
Thank you so much! I was totally overlooking the fact that the numbers are equal. There are 40 students. : )
• Jul 10th 2012, 02:26 AM
kalwin
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