SOLUTION: In a swimming club, the ratio of th number of girls to the number of boys was 5:3. After 3 girls and 5 boys joined the club, the ratio became 7:5. How many girls were there in the

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a swimming club, the ratio of th number of girls to the number of boys was 5:3. After 3 girls and 5 boys joined the club, the ratio became 7:5. How many girls were there in the       Log On


   

Question 1184050: In a swimming club, the ratio of th number of girls to the number of boys was 5:3. After 3 girls and 5 boys joined the club, the ratio became 7:5. How many girls were there in the club at first?
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Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
In a swimming club, the ratio of th number of girls to the number of boys was 5:3.
After 3 girls and 5 boys joined the club, the ratio became 7:5. How many girls were there in the club at first?
~~~~~~~~~~~~~~~~ 

5x girls and 3x boys initially.


After joining


    %285x%2B3%29%2F%283x%2B5%29 = 7%2F5.


To solve, cross multiply. Then simplify


    5*(5x+3) = 7*(3x+5)

    25x + 15 = 21x + 35

    25x - 21x = 35 - 15

       4x     =    20

        x     = 20/4 = 5.


ANSWER.  The number of girls initially was  5x = 5*5 = 25.

Solved.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = number of girls.
let y = number of boys.

original ratio is x/y = 5/3.

second ratio is (x+3)/(y+5) = 7/5.

solve for x in the first ratio to get x = 5y/3.

solve for (x+5) in the second ratio to get (x+3) = 7*(y+5)/5.
simplify to get (x+3) = (7y+35)/5
multiply both sides of that equation by 5 to get 5x+15 = 7y+35
subtract 15 from both sides of that equation to get 5x = 7y+20
replace x with 5y/3 fom the first equation to get 5*5y/3 = 7y+20
simplify to get 25y/3 = 7y+20
multiply both sides by 3 to get 25y = 21y+60
subtract 21y from both sides to get 4y=60
solve for y to get y = 60/4 = 15

the original ratio is x/y = 5/3
when y = 15, the ratio becomes x/15 = 5/3
solve for x to get x = 5*15/3 = 5*5 = 25

you have x = 25 and y = 3
x is the number of girls.
y is the number of boys.

the original ratio is 25/15 = 5/3.
the revised ratio is 28/20 = 14/10 = 7/5.

both ratios are good, confirming the solution is correct.

the solution is there were 25 girls in the club originally.

i did a graphical solution and came up with the same answer.
this is what it looks like.