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GED Math : Proportions and Percentages

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Example Questions

Example Question #61 : Proportions And Percentages

Solve the proportion: $\frac{x}{10} = \frac{5}{2x}$

Possible Answers:

$\pm \frac{1}{4}$

$\pm 2\sqrt5$

$\pm 5$

$\pm \frac{1}{5}$

$\pm 4$

Correct answer:

$\pm 5$

Explanation:

Cross multiply the fractions.

x(2x) = 5(10)

2x^2 =50

Divide by two on both sides.

$\frac{2x^2 }{2}=\frac{50}{2}$

x^2 = 25

Square root both sides.

$\sqrt{x^2 }= \sqrt{25}$

$x=\pm 5$

Verify that both the positive and negative roots will satisfy the solution.

The answer is: $\pm 5$

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Example Question #91 : Complex Operations

What is 25% of 240?

Possible Answers:

215

Correct answer:

Explanation:

To find a percentage of a whole number, we will multiply the two together. So, we get

$25\% \cdot 240$

$\frac{25}{100} \cdot 240$

$\frac{25}{100} \cdot \frac{240}{1}$

Now, the zero in 100 and the zero in 240 can cancel. We get

$\frac{25}{10} \cdot \frac{24}{1}$

$\frac{25 \cdot 24}{10 \cdot 1}$

$\frac{600}{10}$

$\frac{60}{1}$

Therefore, 25% of 240 is 60.

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Example Question #63 : Proportions And Percentages

Solve the proportion: $\frac{3}{x} = \frac{2}{3x+1}$

Possible Answers:

$\frac{1}{9}$

$\frac{5}{8}$

$\frac{3}{7}$

$-\frac{3}{7}$

$\frac{3}{2}$

Correct answer:

$-\frac{3}{7}$

Explanation:

Cross multiply the two fractions.

3(3x+1) = 2x

Distribute the terms on the left.

9x+3 = 2x

Subtract from both sides.

9x+3-9x= 2x-9x

3=-7x

Divide by negative seven on both sides.

$\frac{3}{-7}=\frac{-7x}{-7}$

The answer is: $-\frac{3}{7}$

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Example Question #92 : Complex Operations

Solve the proportion: $\frac{5x}{2} = \frac{4x-1}{3}$

Possible Answers:

$\frac{2}{23}$

$-\frac{2}{23}$

$\frac{2}{7}$

$-\frac{2}{7}$

$-\frac{2}{21}$

Correct answer:

$-\frac{2}{7}$

Explanation:

Cross multiply the two fractions.

5x(3) = 2(4x-1)

Expand both sides.

15x = 8x-2

Subtract on both sides.

15x-8x= 8x-2-8x

7x = -2

Divide by seven on both sides.

$\frac{7x }{7}=\frac{ -2}{7}$

The answer is: $-\frac{2}{7}$

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Example Question #93 : Complex Operations

Solve the proportion: $\frac{x+3}{2} = \frac{2x-9}{3}$

Possible Answers:

Correct answer:

Explanation:

Cross multiply the fractions.

3(x+3) = 2(2x-9)

3x+9 = 4x-18

Subtract from both sides.

3x+9 -3x= 4x-18-3x

9= x-18

Add 18 on both sides.

9+18= x-18+18

27 =x

The answer is:

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Example Question #66 : Proportions And Percentages

Solve the proportion: $\frac{2x-6}{5} = \frac{2}{3}$

Possible Answers:

$-\frac{4}{3}$

$-\frac{3}{4}$

$\frac{14}{3}$

$-\frac{14}{3}$

$\frac{3}{4}$

Correct answer:

$\frac{14}{3}$

Explanation:

Cross multiply the two fractions.

3(2x-6) = 2(5)

Expand both sides.

6x-18 = 10

Add 18 on both sides.

6x-18 +18= 10+18

6x = 28

Divide by 6 on both sides.

$\frac{6x }{6}= \frac{28}{6}$

Reduce both fractions.

The answer is: $\frac{14}{3}$

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Example Question #67 : Proportions And Percentages

On a map, the scale indicates that $1\text{ inch}=15.5\text{ miles}$ . If the distance between two cities is $16.5\text{ inches}$ on the map, how many miles apart are the two cities?

Possible Answers:

102.125

255.75

205.25

290.75

Correct answer:

255.75

Explanation:

From the given information, we can set up the following ratio:

$\frac{1\text{ inch}}{15.5\text{ miles}}=\frac{16.5\text{ inches}}{x\text{ miles}}$ , where is the distance between the two cities.

Now, cross-multiply to solve for .

x=255.75

The two cities are 255.75 miles apart.

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Example Question #68 : Proportions And Percentages

Solve the proportion: $\frac{2x+3}{5} = \frac{8}{7}$

Possible Answers:

$\frac{19}{14}$

$\frac{25}{14}$

$\frac{61}{14}$

$\frac{25}{4}$

$\frac{37}{17}$

Correct answer:

$\frac{19}{14}$

Explanation:

Cross multiply both fractions.

7(2x+3) = 40

Distribute the left side.

14x+21 = 40

Subtract 21 from both sides.

14x+21-21 = 40-21

14x =19

Divide by 14 on both sides.

$\frac{14x}{14} =\frac{19}{14}$

The answer is: $\frac{19}{14}$

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Example Question #431 : Numbers And Operations

What is 18% of $50 ?

Possible Answers:

$\$9$

$\$20$

$\$18$

$\$13$

$\$8$

Correct answer:

$\$9$

Explanation:

To find a percentage of a whole number, we will multiply the two together. So, we get

$18\% \cdot \$50$

$\frac{18}{100} \cdot \$50$

$\frac{18}{100} \cdot \frac{\$50}{1}$

The zero in 100 and the zero in 50 can cancel. We get

$\frac{18}{10} \cdot \frac{\$5}{1}$

$\frac{18 \cdot \$5}{10 \cdot 1}$

$\frac{\$90}{10}$

$\frac{\$9}{1}$

$\$9$

Therefore, 18% of $50 is $9.

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Example Question #70 : Proportions And Percentages

Solve: $\frac{2}{x} = \frac{8}{9}$

Possible Answers:

$\frac{16}{9}$

$\frac{4}{9}$

$\frac{11}{8}$

$\frac{8}{11}$

$\frac{9}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

Cross multiply the two fractions.

2(9) =8x

18 = 8x

Divide by 8 on both sides.

$\frac{18 }{8}= \frac{8x}{8}$

Reduce the fractions.

The answer is: $\frac{9}{4}$

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GED Math : Proportions and Percentages

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #61 : Proportions And Percentages

Example Question #91 : Complex Operations

Example Question #63 : Proportions And Percentages

Example Question #92 : Complex Operations

Example Question #93 : Complex Operations

Example Question #66 : Proportions And Percentages

Example Question #67 : Proportions And Percentages

Example Question #68 : Proportions And Percentages

Example Question #431 : Numbers And Operations

Example Question #70 : Proportions And Percentages

All GED Math Resources

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