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At a certain elementary school, 10 percent of the fifth-gra

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At a certain elementary school, 10 percent of the fifth-gra [#permalink] New post 18 Dec 2017, 12:45
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At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

A. 10%
B. 12%
C. 20%
D. 30%
E. 50%
[Reveal] Spoiler: OA

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Re: At a certain elementary school, 10 percent of the fifth-gra [#permalink] New post 20 Dec 2017, 02:04
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Carcass wrote:
At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

A. 10%
B. 12%
C. 20%
D. 30%
E. 50%



Here let boys = b and girls = g

and total students = 100

i.e. b + g =100 --------- equ 1

10% of the students are member of school band = 10% of 100 = 10 students.

out of which 12% are boys and 8% are girls

i.e. 0.12b + 0.08g = 10 ----------equ 2

Now multiplying equation 1 by 0.12,

0.12b + 0.12g =12 ---------equ 3

equ 2 - equ 3

0.04g = 2

or g = 50

Hence b= 50 (from equation 1)

Therefore there are 50% fifth-grade students at the school are boys. option E
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Re: At a certain elementary school, 10 percent of the fifth-gra [#permalink] New post 29 May 2018, 06:53
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Carcass wrote:
At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?

A. 10%
B. 12%
C. 20%
D. 30%
E. 50%


We can let the total number of 5th grade students be 1000.

So 100 5th graders are in the band.

Now let b = the number of boys in 5th grade of the school, so 1000 - b = the number of girls in 5th grade. We can create the equation:

0.12b + 0.08(1000 - b) = 100

0.12b + 80 - 0.08b = 100

0.04b = 20

b = 20/0.04 = 2000/4 = 500

So the number of boys in 5th grade is 500/1000 = 1/2 = 50% of all 5th graders at the school.

Answer: E
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Re: At a certain elementary school, 10 percent of the fifth-gra   [#permalink] 29 May 2018, 06:53
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