Two Variable Equation Word Problem

AI Thread Summary
The problem involves a club with 15 members, consisting of seniors and juniors, which expands to 25 members after additional seniors and juniors join. The new ratio of juniors to seniors is given as 2:3. To solve for the number of juniors, two equations are established: one representing the total members and another representing the ratio after new members join. The discussion highlights that the original number of members is extraneous information, as only the final total and the ratio are necessary for solving the problem. Ultimately, the focus is on using the equations to determine the number of juniors in the club.
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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.
 
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There are 25 members, 2/5 are junior and 3/5 are senior. Got it?
 
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
 
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.
 
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