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
+128475 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
