How to solve for a variable as part of a fraction - GRE Quantitative Reasoning

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Question

If $\frac{6}{x}=\frac{9}{19}$ , then what is the value of ?

Answer

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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Question

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Answer

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+\[N = (D x 5) + 4\]

=

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

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Question

$\dpi{100} \small \frac{4 }{x} = \frac{2}{25}$

Find x.

Answer

Cross multiply:

$\dpi{100} \small 4 \times 25 = 2x$

$\dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$

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Question

If $\frac{(x-7)}{2x} = \frac{5}{9}$ , what is the value of ?

Answer

Start by cross multiplying to get the equation

$5\cdot2x=(x-7)\cdot 9$

.

Then simplify by subtracting from each side to get the solution,

.

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Question

If $\frac{x}{4} = 15$ , then what is $\frac{3x}{5} - 36$ equal to?

Answer

We start by solving for x in $\frac{x}{4} = 15$ by multiplying 4 and 15, which gives us .

Then substituting 60 for x in,

$\frac{3x}{5} - 36$ gives us

$\frac{180}{5} - 36=36-36=0$ which equals 0.

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Question

If $\frac{x-p}{r} = \frac{q}{pr}$ , and , what is the value of ?

Answer

Start by cross multiplying which gives us .

Simplify by dividing both sides by which gives us .

Isolate by dividing both sides by and then adding to both sides, which gives us $x = \frac{q}{p} +p$ .

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Question

If $\frac{2}{3x} = \frac{4x}{5}$ , and what is the value of ?

Answer

Start by cross multiplying which gives us

$12x^{^{2}} = 10$ .

Divide both sides by 12 and simplify which gives us $x^{^{2}} = \frac{5}{6}$ .

Since , we only take the positive square root as the solution, ${}x = {\sqrt{\frac{5}{6}}}$ .

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