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In a swimming club, the ratio of girls to boys is 5:3. After 3 more girls and 5 more boys joined the club this spring, the ratio became 7:5. How many boys and girls total were in the club before spring

 Jan 16, 2020
 #1
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Call x  the number of original girls

Call y the number of original boys

 

And we know that

 

x / y  =  5 /3   cross-multiply

 

3x =  5y

x  =  (5/3)y    (1)

 

And we also know that

 

x+ 3                 7

_______  =    ___          sub (1)  in for x

y + 5                5

 

(5/3)y + 3            7

________  =     ___       cross-multiply

y +  5                  5

 

 

 

5 ([ 5/3]y + 3 ]  =  7 [ y + 5]

 

(25/3)y + 15  =  7y   +  35       subtract  15, 7y from both sides

 

( 25/3  - 7) y  = 20

 

(25/3 - 21/3)y  = 20

 

(4/3)y   =  20         multiply both sides by 3/4

 

y = 20(3)/4  =   15   = original number of  boys

 

And 

 

3x  = 5y

 

3x  = 5 *15

 

3x  = 75     divide both sides by  3

 

x  = 25 =  original number of girls

 

 

cool cool cool

 Jan 16, 2020

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