SOLUTION: I have this problem in my textbook and I have been struggling to find a way to solve it, although it had been solved already on this website but I don't understand how the answer p

Question 1172785: I have this problem in my textbook and I have been struggling to find a way to solve it, although it had been solved already on this website but I don't understand how the answer provider was able to solve it. Anyways here's the problem.

In a certain mathematics class, the part of the class that are members of the math club is 50% of
the rest of that class. The total number of math club members in this class is what percent of the
entire class?

Thanks :)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's how it works, as far as i can see.
let m = the number of members of the math club.
let t = the number of member in the whole class.
this includes the members of the math club as well as the members who are not in the math club.
the number of members who are not in the math club are equal to t - m.
you are told that the number of members of the math club are 50% of the members of the class that are not members of the math club.
the equation for that would be:
m = .50 * (t - m).
simplify this equation to get:
m = .50 * t - .50 * m
add .50 * m to both sides of this equation to get:
m + .50 * m = .50 * t
combine like terms to get:
1.5 * m = .50 * t
divide both sides of this equation by .5 to get:
1.5 / .5 * m = t
simplify this to get:
3 * m = t
divide both sides to get:
m = 1/3 * t
that's your answer.
to confirm, do the following.
m = 1/3 * t
this means that (t - m) = 2/3 * t
m / (t - m) = (1/3) / (2/3) = 1/2 = .5
this means that the number of members of the math club is 1/2 * the members of the class that are not members of the math club.

an example might help solidify understanding of the solution.
suppose the total class had 120 members.
assume that 2/3 of the class are not members of the math club.
that makes 80 members of the class that are not members of the math club.
that also makes 1/3 of the class that are members of the math club.
1/3 * 120 = 40 members of the math club.
you have 40 members of the class who are members of the math club and 80 members of the class who are not members of the math club.
40/80 = .5 = .50
the numbers of the class who are members of the math class is equal to 50% of the members of the class who are not members of the math class.

if you still have trouble understanding, let me know and i'll try harder.
theo
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