SOLUTION: A school has 630 students. The ratio of the number of boys to the number of girls is 3:2. This ratio changes to 7:5 after the admission of 90 new students. Find the number of newly

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Question 1086282: A school has 630 students. The ratio of the number of boys to the number of girls is 3:2. This ratio changes to 7:5 after the admission of 90 new students. Find the number of newly admitted boys.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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A school has 630 students. The ratio of the number of boys to the number of girls is 3:2.
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system%28x%2By=630%2Cy%2Fx=3%2F2%29

x%2B3x%2F2=630
2x%2B3x=1260
5x=1260
girls, x=252,
boys, y=378



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This ratio changes to 7:5 after the admission of 90 new students.
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b, boys added
g, girls added
system%28%28b%2B378%29%2F%28g%2B252%29=7%2F5%2Cb%2Bg=90%29
5%28b%2B378%29=7%28g%2B252%29
5b%2B1890=7g%2B1764
7g-5b=1890-1764
7g-5b=126
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7g-5%2890-g%29=126
7g-450%2B5g=126
12g=126%2B450
12g=576
g=48------the added girls
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highlight%28b=42%29-----the added boys

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A school has 630 students. The ratio of the number of boys to the number of girls is 3:2. This ratio changes to 7:5 after the admission of 90 new students. Find the number of newly admitted boys.
Number of boys, initially: matrix%281%2C3%2C+%283%2F5%29+%2A+630%2C+%22=%22%2C+378%29

With 90 students being added, the number of students become: 720 (630 + 90)

Number of boys after new admissions: matrix%281%2C3%2C+%287%2F12%29+%2A+720%2C+%22=%22%2C+420%29

Number of newly admitted boys: highlight_green%28matrix%281%2C3%2C+420+-+378%2C+%22=%22%2C+highlight%2842%29%29%29

It is that easy! Nothing COMPLEX/CONFUSING!