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GED Math : Complex Operations

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Example Questions

Example Question #431 : Numbers And Operations

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 #432 : Numbers And Operations

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

Possible Answers:

$\frac{8}{11}$

$\frac{16}{9}$

$\frac{9}{4}$

$\frac{4}{9}$

$\frac{11}{8}$

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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Example Question #433 : Numbers And Operations

What is $136\%$ of ?

Possible Answers:

27.08

21.76

19.36

26.66

Correct answer:

21.76

Explanation:

Start by converting $136\%$ to a decimal. To do this, move the decimal point to the left to spaces.

$136\%=1.36$

Now multiply by .

$1.36\times 16=21.76$

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Example Question #434 : Numbers And Operations

Solve the proportion: $\frac{5}{2x} = \frac{8}{9}$

Possible Answers:

$\textup{No solution.}$

$\frac{45}{16}$

$\frac{9}{2}$

$\frac{7}{6}$

$\frac{6}{7}$

Correct answer:

$\frac{45}{16}$

Explanation:

Cross multiply the two fractions.

5(9) = 8(2x)

45 = 16x

Divide by 16 on both sides.

$\frac{45}{16} = \frac{16x}{16}$

The answer is: $\frac{45}{16}$

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Example Question #71 : Proportions And Percentages

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

Possible Answers:

$\frac{8}{5}$

$\frac{5}{8}$

$\frac{21}{16}$

$\frac{28}{3}$

$\frac{21}{10}$

Correct answer:

$\frac{21}{16}$

Explanation:

Cross multiply the two terms.

7(3) = 8(2x)

Simplify the terms.

21 = 16x

Divide by 16 on both sides.

$\frac{21}{16} = \frac{16x}{16}$

The answer is: $\frac{21}{16}$

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Example Question #432 : Numbers And Operations

Solve the proportion: $\frac{7}{x} = \frac{4}{9}$

Possible Answers:

$\frac{28}{9}$

$\frac{63}{4}$

Correct answer:

$\frac{63}{4}$

Explanation:

Cross multiply both fractions.

7(9) = 4x

Divide by four on both sides.

$\frac{7(9)}{4} = \frac{4x}{4}$

The answer is: $\frac{63}{4}$

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Example Question #433 : Numbers And Operations

Solve the proportion: $\frac{8}{3x+1} = \frac{5}{x}$

Possible Answers:

$-\frac{5}{7}$

$-\frac{10}{7}$

$-\frac{1}{7}$

$-\frac{10}{23}$

$-\frac{1}{5}$

Correct answer:

$-\frac{5}{7}$

Explanation:

Cross multiply the two fractions.

8x = 5(3x+1)

Simplify the right side.

8x =15x+5

Subtract 15x on both sides.

8x-15x =15x+5-15x

-7x = 5

Divide by negative seven on both sides.

$\frac{-7x }{-7}= \frac{5}{-7}$

The answer is: $-\frac{5}{7}$

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Example Question #434 : Numbers And Operations

To make a certain shade of green, the blue paint and the yellow paint must be mixed in a ratio of 3:5 . If a painter uses gallons of yellow paint, how many gallons of blue paint must be used to create this shade of green?

Possible Answers:

8.8

13.4

10.2

12.6

Correct answer:

10.2

Explanation:

Let be the gallons of blue paint needed. We can setup the following equation using the given ratio.

$\frac{3}{5}=\frac{x}{17}$

Cross-multiply and solve for .

5x=51

x=10.2

The painter must use 10.2 gallons of blue paint.

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GED Math : Complex Operations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #431 : Numbers And Operations

Example Question #68 : Proportions And Percentages

Example Question #431 : Numbers And Operations

Example Question #432 : Numbers And Operations

Example Question #433 : Numbers And Operations

Example Question #434 : Numbers And Operations

Example Question #71 : Proportions And Percentages

Example Question #432 : Numbers And Operations

Example Question #433 : Numbers And Operations

Example Question #434 : Numbers And Operations

All GED Math Resources

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