SOLUTION: the ratio of females to males in a school band is 7 to 4. if 3 females and 12 males are absent from practice, the ratio of females to males is 5 to 2. how many members of the band

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: the ratio of females to males in a school band is 7 to 4. if 3 females and 12 males are absent from practice, the ratio of females to males is 5 to 2. how many members of the band       Log On


   

Question 178124: the ratio of females to males in a school band is 7 to 4. if 3 females and 12 males are absent from practice, the ratio of females to males is 5 to 2. how many members of the band attend practice?
Found 2 solutions by josmiceli, gonzo:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
let f= number of females in the school band
Let m= number of males in the school band
given:
(1) f%2Fm+=+7%2F4
(2) %28f-3%29%2F%28m-12%29+=+5%2F2
Multiply both sides of (2) by 2%2A%28m-12%29
%28f-3%29%2F%28m-12%29+=+5%2F2
2%2A%28f-3%29+=+5%2A%28m-12%29
2f+-+6+=+5m+-+60
(3) 2f+-+5m+%2B+54+=+0
Multiply both sides of (1) by 4m
f%2Fm+=+7%2F4
4f+=+7m
(4) 4f+-+7m+=+0
Multiply both sides of (3) by 2 and subtract
(4) from (3)
(3) 4f+-+10m+%2B+108+=+0
(4) -4f+%2B+7m+=+0
-3m+%2B+108+=+0
3m+=+108
m+=+36
And, since
(1) f%2Fm+=+7%2F4
f%2F36+=+7%2F4
Multiply both sides by 36
f+=+7%2A9
f+=+63
The total number of students in the band is 36+%2B+63+=+99,
but the problem wants to know the number of members that
attended practice
For females, that would be
f+-+3+=+63+-+3
63+-+3+=+60
For males,
m+-+12+=+36+-+12
36+-+12+=+24
60+%2B+24+=+84 members attended practice
check answer:
(1) f%2Fm+=+7%2F4
63%2F36+=+7%2F4
63%2A4+=+7%2A36
252+=+252
(2) %28f-3%29%2F%28m-12%29+=+5%2F2
%2863-3%29%2F%2836-12%29+=+5%2F2
60%2F24+=+5%2F2
2%2A60+=+5%2A24
120+=+120
OK

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
f/m = 7/4
multiply both sides of this eqution to get:
f = 7m/4
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(f-3)/(m-12) = 5/2
multiply both sides of this equation by (m-12) to get:
f-3 = 5(m-12)/2
substitute 7m/4 for f to get:
7m/4 - 3 = 5(m-12)/2
multiply both sides of this equation by 4 to get:
7m - 3*4 = 4*5*(m-12)/2
simplify to get:
7m - 12 = 10m - 120
subtract 7m from both sides of this equation and add 120 to both sides of this equation to get:
120 - 12 = 10m - 7m
simplify to get:
108 = 3m
divide both sides of this equation by 3 to get:
m = 36
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f = 7/4 * m = 7/4 * 36 = 63
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there are 63 females and 36 males in the band.
total members in the band is 63 + 36 = 99
63/36 = 7/4
ratio for the full band is good.
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63-3 = 60
36-12 = 24
60 females attended practice and 24 males attended practice.
total members who attended practice are 60 + 24 = 84
60/24 = 5/2
ratio for the members of the band that attend practice is good.
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your answer is:
84 members of the band attended practice.
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