90 students represent x percent of the boys at Jones Element

\(90\) 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;

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

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

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

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

Answer (B)...

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.

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Using algebra
90=x/100*40/100*x=>x^2 = 9*10000/4 = > x = 300/2 => x = 150!

Let the number of boys = b. We can create the equation:

90 = b * x/100

and

b = 0.4x

Substituting 0.4x for b in the first equation, we have:

90 = 0.4x * x/100

9000 = 0.4x^2

22500 = x^2

150 = x

Answer: B

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

#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

this was a very very good question......it made me read the sentence carefully (i got it wrong tho)

90 is NOT the number of boys!
its just a number
and then the question is understood and the arithmetic is simple!

Great explanatin Bunuel, not sure why is the same variable x here being used in x percent and x student while it has different meaning here? I got confused by this.
Could you help clarify thanks.

Let's break down the information given in the problem:

90 students represent x percent of the boys at Jones Elementary School.
The boys at Jones Elementary make up 40% of the total school population of x students.
Let's use algebra to solve for x.

Let's assume that B is the total number of boys at Jones Elementary School, and T is the total school population.

From the first statement, 90 students represent x percent of the boys at Jones Elementary School. So we can write this as:

90 = (x/100) * B

From the second statement, the boys at Jones Elementary make up 40% of the total school population of x students. So we can write this as:

B = (40/100) * x

Now, we have two equations:

90 = (x/100) * B
B = (40/100) * x
Since we have two equations and two unknowns (x and B), we can solve for x.

First, let's solve for B in terms of x from the second equation:

B = (40/100) * x
B = (2/5) * x

Now, we can substitute this value of B into the first equation:

90 = (x/100) * B
90 = (x/100) * ((2/5) * x)

Now, simplify the equation:

90 = (2x^2/500)

Next, let's solve for x:

90 * 500 = 2x^2
45000 = 2x^2
x^2 = 45000 / 2
x^2 = 22500

Now, take the square root of both sides to find the positive value of x:

x = √22500
x ≈ 150.0

So, the total school population (x) is 150 students.

Hence B

The variable 'x' in this problem is indeed used to represent two different things - it's stated that 90 students constitute x percent of the boys and that the total student population is x. When we solve the problem, we find that 'x' is 150. Hence, we find that 90 students represent 150 percent of the boys (indicating there are 60 boys), and that the total student count is 150. Therefore, these two different quantities are equal in this case.

Great explanation always thanks Bunuel

Let there be B boys.

Then we have -> \(\frac{x}{100}\) * B = 90 --- (1)

Also, \(\frac{40}{100}\) * x = B --- (2)

Using (1) and (2), we get --> \(x^2\) = \(\frac{900}{4}\) = 150.

Answer: B.