# Two Variable Equation Word Problem

1. May 22, 2005

### homegrown898

A club consisting of seniors and juniors has 15 members. After seven more seniors and three more juniors join the club, the ratio of juniors to seniors is 2:3. How many juniors are in the club?

I guess the thing that screws me up is the ratio part. I don't know what to do. I've found a negative number for J but that can't be right. Right now, I think there are 10 juniors in the club but I really don't know how to prove that. I kind of came upon that number accidentally.

2. May 22, 2005

### mathman

There are 25 members, 2/5 are junior and 3/5 are senior. Got it?

3. May 22, 2005

### b0mb0nika

10 sounds right

put the problem in mathematical terms:
juniors = j , seniors = s
j+s=15.........................(1)
3 more juniors and 7 more seniors join.. so we'll have j+3 juniors and s+7 seniors
now the ratio of new j to new s is 2:3
that means :
j+3/s+7 = 2/3....................(2)

so now u have 2 equations (1) and (2) with 2 unknowns that u can solve to find out what j equals to

4. May 23, 2005

### mathman

The main difficulty with the original problem information is that there is unneccesary information. All you need is a total of 25 members and the 2:3 ratio of juniors to seniors. The fact that there were originally 15 members and seven added seniors and seven added juniors is extraneous. The only point would be if the question was how many of the original 15 were juniors or seniors.