Expert: Bobby Soltani - 10/14/2004

Question
Hi Bobby,

How do I go about finding the number of women on a committee? Thanks in advance.

harraine

Question:
If the ratio of men to women on a committee of 20 members is 3 to 2, how many members of the committee are women?  

Answer
Hi Harraine,

In this problem, we create two equations and two unknowns.  When we do that, we can solve them.  Let's create the two equations.

1.  committee of 20 members.  The number of men(m) plus the number of women(w) is equal to 20

m + w = 20

2.  the ratio of men to women is 3 to 2.  When you say the ratio of something is x to y, you can right it as x/y.

(m/w) = (3/2)

Now we have two equations.  Let's solve the second one for w.

(m/w) = 3/2
multiply both sides by w
m = 3w/2
multiply both sides by 2/3
2m/3 = w or w = (2/3)*m

now we can plug this value for w into the first equation and solve it for m

m + (2/3)*m = 20
m is the same as (3/3)*m
(3/3)*m + (2/3)*m = 20
add the fractions
(5/3)*m = 20
multiply both sides by 3/5
m = 12

if m = 12, we know that m+w = 20, so w = 8.

That is, there are 8 women on the commitee.  I hope this helps you out.  Let me know if you have any questions.

Bobby