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PSAT Math : How to solve for a variable as part of a fraction

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Example Question #3241 : Sat Mathematics

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

Possible Answers:

none of these

3/38

9/114

38/3

7/12

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

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

Find x.

Possible Answers:

$\dpi{100} \small \frac{8}{25}$

$\dpi{100} \small 0.25$

$\dpi{100} \small 50$

None

$\dpi{100} \small \frac{25}{8}$

Correct answer:

$\dpi{100} \small 50$

Explanation:

Cross multiply:

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

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

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

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Example Question #3 : How To Solve For A Variable As Part Of A Fraction

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.

Possible Answers:

$\frac{1}{2}$

$\frac{1}{3}$

Correct answer:

Explanation:

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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Example Question #11 : How To Solve For A Variable As Part Of A Fraction

Solve for :

$\frac{24x-8}{3}=12$

Possible Answers:

$\frac{1}{5}$

$3\frac{1}{4}$

$1\frac{5}{6}$

$2\frac{7}{8}$

Correct answer:

$1\frac{5}{6}$

Explanation:

Solve for :

$\frac{24x-8}{3}=12$

Step 1: Cross-multiply to eliminate the fraction

$3(\frac{24x-8}{3})=12 \cdot 3$

24x-8 = 36

Step 2: Solve for :

24x=44

$x=\frac{44}{24}=\frac{22}{12}=\frac{11}{6}=1\frac{5}{6}$

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PSAT Math : How to solve for a variable as part of a fraction

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #3241 : Sat Mathematics

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #3 : How To Solve For A Variable As Part Of A Fraction

Example Question #11 : How To Solve For A Variable As Part Of A Fraction

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