SOLUTION: The ratio of females to males in a school band is 7 to 4. If three females and twelve males are absent from practice, the ratio of females to males is 5 to 2. How many members of
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Question 122851: The ratio of females to males in a school band is 7 to 4. If three females and twelve males are absent from practice, the ratio of females to males is 5 to 2. How many members of the band attended practice? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The ratio of females to males in a school band is 7 to 4. If three females and twelve males are absent from practice, the ratio of females to males is 5 to 2. How many members of the band attended practice?
:
Let x = boys
Let y = girls;
:
It says,"The ratio of females to males in a school band is 7 to 4." so we can say: =
Cross multiply
7x = 4y
or
7x - 4y = 0
:
If three females and twelve males are absent from practice, the ratio of females to males is 5 to 2. How many members of the band attended practice? =
Cross multiply
5(x-12) = 2(y-3)
5x - 60 = 2y - 6
5x - 2y = +60 - 6
5x - 2y = 54
:
Use elimination; Mult the 2nd equation by 2; subtract the 1st equation
10x - 4y = 108
7x - 4y = 0
---------------- subtracting eliminates y
3x + 0y = 108
x =
x = 36 boys
:
Find the girls
7(36) = 4y
252 = 4y
y =
y = 63 girls
:
But it asked how many attended practice:
(36-12) + (63-3) = 84 kids
:
Check: reduces to
and reduces to
