SOLUTION: How many boys are there in a group of 27 students if there are four-fifths as many girls as there are boys? A)8 B)10 C)12 D)15

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Question 1143742: How many boys are there in a group of 27 students if there are four-fifths as many girls as there are boys?
A)8
B)10
C)12
D)15
Found 3 solutions by ikleyn, Edwin McCravy, greenestamps:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

%284%2F5%29boys + boys = 27,


%284%2F5%29b + b = 27


4b + 5b = 27*5 


9b = 27*5


b = 3*5 = 15.      ANSWER


CHECK.  15+%2B+%284%2F5%29%2A15 = 15 + 12 = 27.    ! Correct !


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
How many boys are there...
matrix%281%2C3%2CB%2C%22%22=%22%22%2C%22%3F%22%29
...in a group of 27 students...
matrix%281%2C3%2CB%2BG%2C%22%22=%22%22%2C27%29
...if there are four-fifths as many girls as there are boys?
matrix%281%2C3%2CG%2C%22%22=%22%22%2Cexpr%284%2F5%29B%29
Substitute expr%284%2F5%29B for G in

matrix%281%2C3%2CB%2BG%2C%22%22=%22%22%2C27%29

matrix%281%2C3%2CB%2Bexpr%284%2F5%29B%2C%22%22=%22%22%2C27%29

Multiply every term on both sides by the LCD, which is 5:

matrix%281%2C3%2C5%2AB%2B5%2Aexpr%284%2F5%29B%2C%22%22=%22%22%2C5%2A27%29

matrix%281%2C3%2C5B%2Bcross%285%29expr%284%2Fcross%285%29%29B%2C%22%22=%22%22%2C5%2A27%29

matrix%281%2C3%2C5B%2B4B%2C%22%22=%22%22%2C135%29

matrix%281%2C3%2C9B%2C%22%22=%22%22%2C135%29

Divide both sides by 9:

matrix%281%2C3%2C9B%2F9%2C%22%22=%22%22%2C135%2F9%29

matrix%281%2C3%2CB%2C%22%22=%22%22%2C15%29

There are 15 boys.

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Given that there are 4/5 as many girls as boys, you can treat the "4/5" as a ratio -- girls:boys = 4:5. So use the general procedure for setting up a problem involving ratios:

let 4x = # of girls
let 5x = # of boys

Then

4x%2B5x+=+9x+=+27
x+=+3

The number of boys is 5x = 5(3) = 15.