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90 students represent x percent of the boys at Jones

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90 students represent x percent of the boys at Jones [#permalink] New post 26 Aug 2007, 10:07
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51% (02:06) correct 49% (00:55) wrong based on 132 sessions
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

A. 125
B. 150
C. 225
D. 250
E. 500

OPEN DISCUSSION OF THIS QUESTION IS HERE: 90-students-represent-x-percent-of-the-boys-at-jones-element-145335.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Jun 2014, 02:09, edited 1 time in total.
Edited the question and added the OA
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Re: PS - nice one [#permalink] New post 26 Aug 2007, 10:34
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Piter wrote:
90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?
125
150
225
250
500


150

Total boys at Jones School = J
Equation 1: (x/100) * J = 90 => J = 9000/x
Total school population = x
Equation 2: (J/x)*100 = 40

Using equation 1 and 2, plug in
(9000/x/x)*100 = 40
=> x^2 = (9000*100)/40 = 25*9*100
x = 5*3*10 = 150
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 [#permalink] New post 26 Aug 2007, 10:38
90 = (x/100)*(# boys)

# boys = .4x

substitute and solve:
90 = (x/100)*(.4x)
9000 = .4(x^2)
25000 = x^2
x=150

Answer: B
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 [#permalink] New post 26 Aug 2007, 11:36
same here - the answer is (B) - the double use of x both for percentage and for the total number of students can be deceiving.

90 = x/100*0.4x

9,000 = x^2*0.4

22,500 = x^2

x = 150

:-D
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Re: 90 students represent x percent of the boys at Jones [#permalink] New post 08 Jun 2014, 00:13
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Re: 90 students represent x percent of the boys at Jones [#permalink] New post 08 Jun 2014, 02:10
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90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 40% of the total school population of x students, what is x?

A. 125
B. 150
C. 225
D. 250
E. 500

Step by step:
90 students represent x percent of the boys at Jones Elementary School: \(90=\frac{x}{100}*boys\) --> \(boys=\frac{9000}{x}\);

The boys at Jones Elementary make up 40% of the total school population of x students: \(boys=0.4x\) --> \(\frac{9000}{x}=0.4x\) --> \(x=150\).

Answer: B.

To elaborate: there are total of 150 students at the school and 0.4*150=60 of them are boys. 150% of 60 boys is 90.

OPEN DISCUSSION OF THIS QUESTION IS HERE: 90-students-represent-x-percent-of-the-boys-at-jones-element-145335.html
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Re: 90 students represent x percent of the boys at Jones   [#permalink] 08 Jun 2014, 02:10
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