At Annville Junior High School, 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?

Mr.Owl Oct 21, 2017

#1**+2 **

There are 15 people in the science club.

80% of the people in the science club are in both the science and math clubs, so...

number of people in both clubs = 0.8 * 15 = 12

Let the number of people in math club = m

30% of the people in the math club are in both the science and math clubs,

and remember there are 12 people that are in both clubs, so...

0.3m = 12

m = 12 / 0.3

m = 40

hectictar Oct 21, 2017

#2**+3 **

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

Note that 80% = 4/5....so 4/5 * 15 = 60/ 5 = 12

So....12 students in the Science Club are Math Club members

And these 12 represent 30% of the Math Club

Call the total members in the Math Club, M

So.....

30% of M = 12 or, put another way

.30 M = 12 divide both sides by .30

M = 12 / .30 = 40 students in the Math Club

CPhill Oct 21, 2017