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In math club, there were 8 girls for every 5 boys. when 19 boys and 4 girls were added, the ratio became 9 girls for every 7 boys, how many girls were there at the start?

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by acel1234

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by acel1234

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The first ratio is 32:30 = (32+4) (30+19)= 36:49

Boys: 5x

When 4 girls and 19 boys are added/joined, the ratio became 9:7

Solution:

(8x + 4) : (5x + 19) = 9 : 7

7 (8x + 4) = 9 (5x + 19)

56x + 28 = 45x + 171

56x - 45x = 171 - 28

11x = 143

11x/11 = 143/11

x = 13

Original Number of students:

104 : 65 = 8 : 5 (in lowest term, GCF of 104 and 65 is 13.)

Check:

When 4 girls and 19 boys are added/joined, the ratio becomes 9:7.

Girls: 104 + 4 = 108

Boys: 65 + 19 = 84

108 : 84 = 9: 7 (in lowest term, GCF of 108 and 84 is 12.)