SOLUTION: There were twice as many boys as girls in a Swimming Club. After 40 boys and 15 girls left the club, the number of girls who remained was 3/5 of the number of boys who remained in

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Question 1201509: There were twice as many boys as girls in a Swimming Club. After 40 boys and 15 girls left the club, the number of girls who remained was 3/5 of the number of boys who remained in the club. How many children were there in the club at first?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 135


Work Shown:

x = number of girls initially
2x = number of boys initially

40 boys leave
2x becomes 2x-40

15 girls leave
x becomes x-15

"number of girls who remained was 3/5 of the number of boys who remained in the club" tells us that
x - 15 = (3/5)*(2x-40)
5(x - 15) = 3(2x-40)
5x - 75 = 6x-120
5x-6x = -120+75
-x = -45
x = 45 girls initially
which leads to
2x = 2*45 = 90 boys initially

45+90 = 135 is the final answer.

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Check:
90 boys at first
40 boys leave
90-40 = 50 boys left

45 girls at first
15 girls leave
45-15 = 30 girls left
ratio of girls remaining to boys remaining is 30/50 = 3/5, which confirms the answer is correct.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
There were twice as many boys as girls in a Swimming Club.
After 40 boys and 15 girls left the club, the number of girls who remained
was 3/5 of the number of boys who remained in the club.
How many children were there in the club at first?
~~~~~~~~~~~~~~~~~~~ 

Originally  x girls ans 2x boys.
The number x is unknown, and our goal is to find x.


Agter After 40 boys and 15 girls left the club,
(x-15) girls and (2x-40) boys remained.


The problem dictates us this proportion

    %28x-15%29%2F%282x-40%29 = 3/5.


To solve it, first cross multiply

    5(x-15) = 3*(2x-40).


Next simplify and find x

    5x - 75 = 6x - 120

    120 - 75 = 6x - x

       45    =    x.


ANSWER.  Originally, there were 45 girls and 2*45 = 90 boys.

         The total was 45 + 90 = 135 children.

Solved.