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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?

Sagot :

ANSWER:  There were 104 girls in Math Club at the start.

At the start, the ratio of girls is to boys is 8:5

Girls: 8x
Boys: 5x

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

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

[tex] \frac{8x + 4}{5x + 19} = \frac{9}{7} [/tex]

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

ANSWER:  There were 104 girls in Math Club at the start.

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.)
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