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# 90 students represent x percent of the boys at Jones Element

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90 students represent x percent of the boys at Jones Element [#permalink]

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06 Jan 2013, 09:31
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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

[cant understand the language]
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Jan 2013, 01:46, edited 1 time in total.
Renamed the topic and edited the question.
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06 Jan 2013, 09:39
vidyavatigore 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?

[cant understand the language]

125

150

225

250

500

$$90=x/100 * # boys$$
#boys=$$0.4x$$
$$90=x/100 * 0.4x$$.
$$9000=0.4* x^2$$
$$22500=x^2$$
$$x=150$$
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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07 Jan 2013, 01:56
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vidyavatigore 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?

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

[cant understand the language]

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: $$boys=0.4x$$ --> $$\frac{9000}{x}=0.4x$$ --> $$x=150$$.

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.
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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28 Nov 2014, 11:41
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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04 Apr 2016, 06:25
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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28 Aug 2016, 07:36
backsolve some answer choices :--
let us take x= 500 , 40% of these represents boys . Ok this implies boys = 200. But does 500% of 200 = 90? 500% of 200 =1000. so this does not work. Actually this tells us that we need something small.

let us take x=150. 40% of 150 = 60 . So boys = 60. 150% of boys = 3/2*60 = 90!. This works.

**********************************
Using algebra
90=x/100*40/100*x=>x^2 = 9*10000/4 = > x = 300/2 => x = 150!
Re: 90 students represent x percent of the boys at Jones Element   [#permalink] 28 Aug 2016, 07:36
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# 90 students represent x percent of the boys at Jones Element

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