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

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Intern
Joined: 06 Dec 2012
Posts: 1
90 students represent x percent of the boys at Jones Element [#permalink]

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Updated on: 07 Jan 2013, 02:46
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Difficulty:

45% (medium)

Question Stats:

66% (01:24) correct 34% (01:25) wrong based on 278 sessions

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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]

Originally posted by vidyavatigore on 06 Jan 2013, 10:31.
Last edited by Bunuel on 07 Jan 2013, 02:46, edited 1 time in total.
Renamed the topic and edited the question.
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06 Jan 2013, 10:39
1
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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Posts: 47015
Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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07 Jan 2013, 02:56
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1
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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Posts: 102
Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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28 Aug 2016, 08:36
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!
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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07 Jun 2017, 16:13
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]

The key to understanding this question is understanding that x is constant- in other words- the total number of students as represented by X must equal the the percentage of increase of some number must be to equal 90.

150 (.4) = 60 boys

90= 60 boys (150%) (naturally, applying real world thinking, we might typically think that the actual number of boys would be some number greater than 90 but we could perhaps rationalize the practicality of this problem with the following example- if a certain school needs to expand it's population of minority students to a certain percentage increase of minority students at that school).

90 boys represent 150% of the boys at this high- it's kind of a weird question - also it's important to note a 150% increase of some number is NOT equal to 150% of that number
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Joined: 09 Oct 2016
Posts: 35
Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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28 Jul 2017, 08:48
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]

#of Boys = X(40/100)
90 = (X/100)(40X/100)
90 = ((4X^2)/ 1000)
X^2 = 90000/4 ---- take the root square for both sides
X= 300/4
X = 150
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Re: 90 students represent x percent of the boys at Jones Element [#permalink]

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18 Aug 2017, 23:14
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]

$$90$$ students represent $$x$$ percent of the boys at Jones Elementary School.

$$90 = x$$% of Boys $$= (\frac{x}{100})$$ Boys ------ (i)

Boys at Jones Elementary make up $$40$$% of the total school population of $$x$$ students.

Boys $$= 40$$% of $$x = (\frac{40}{100})x$$

Boys $$= (\frac{2}{5})x$$ ------- (ii)

Substituting Value of Boys from (ii) into (i), we get;

$$90 = (\frac{x}{100}) (\frac{2}{5})x$$

$$\frac{(x^2)(2)}{(100)(5)} = 90$$

$$x^2 = \frac{(90)(100)(5)}{2} = 45*5*100$$

$$x = \sqrt{45*5*100} = 3*5*10 = 150$$

Re: 90 students represent x percent of the boys at Jones Element   [#permalink] 18 Aug 2017, 23:14
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