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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #79 : Converting Measurements

Convert $\textup{54 inches}$ to $\textup{feet}$ .

Possible Answers:

$\frac{5}{12}\textup{ feet}$

$4.5 \textup{ feet}$

$30 \textup{ feet}$

$\textup{20 feet}$

$\frac{12}{5} \textup{ feet}$

Correct answer:

$4.5 \textup{ feet}$

Explanation:

There are twelve inches in a foot. Write the dimensional analysis.

$12 \textup{ inches } = 1\textup{ foot}$

To get an answer in feet, we will need to eliminate the inches dimension.

$54\textup{ inches}\left (\frac{1 \textup{ foot}}{12 \textup{ inches}} \right )$

The answer is: $4.5\textup{ feet}$

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Example Question #80 : Converting Measurements

Convert $60\textup{ inches}$ to $\textup{feet}$ .

Possible Answers:

$20\textup{ feet}$

$5\textup{ feet}$

$300\textup{ feet}$

$\frac{5}{12}\textup{ feet}$

$\frac{12}{5}\textup{ feet}$

Correct answer:

$5\textup{ feet}$

Explanation:

There are twelve inches in a foot. Write the dimensional analysis.

$12 \textup{ inches } = 1\textup{ foot}$

To get an answer in feet, we will need to eliminate the inches dimension.

$60 \textup{ inches}(\frac{1 \textup{ foot}}{12 \textup{ inches}})$

The answer is: $5\textup{ feet}$

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Example Question #81 : Converting Measurements

Convert three inches to a foot.

Possible Answers:

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{36}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

There are twelve inches in a foot.

$12\textup{ inches} = 1\textup{ foot}$

Multiply the given dimension by the conversion.

$3\textup{ inches }(\frac{1\textup{ foot }}{12\textup{ inches}}) = \frac{3}{12}\textup{ foot}$

Reduce the fraction.

The answer is: $\frac{1}{4}\textup{ foot}$

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Example Question #81 : Converting Measurements

Convert four inches to yards.

Possible Answers:

$\frac{2}{7}$

$\frac{1}{12}$

$\frac{1}{18}$

$\frac{1}{9}$

$\frac{2}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

Before we can convert this, we will need the conversion factors from inches to feet and feet to yards.

$12\textup{ inches }= 1\textup{ foot}$

$3 \textup{ feet}= 1\textup{ yard}$

Multiply four inches with the dimensional analyses to get the final dimension in yards.

$4\textup{ inches}( \frac{ 1\textup{ foot}}{12\textup{ inches }})(\frac{1\textup{ yard}}{3 \textup{ feet}})$

The feet and inches dimensions will cancel and yards will be the only dimension.

Simplify the expression.

$4( \frac{ 1}{12})(\frac{1\textup{ yard}}{3 }) = \frac{4 \textup{ yard}}{36 } = \frac{1}{9} \textup{ yard}$

The answer is: $\frac{1}{9}$

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Example Question #82 : Converting Measurements

Convert 64 inches to feet.

Possible Answers:

$\frac{1}{768}$

768

$\frac{3}{16}$

$\frac{16}{3}$

$\frac{75}{4}$

Correct answer:

$\frac{16}{3}$

Explanation:

There are 12 inches in a foot. Set up a proportion.

$\frac{12\textup{ inches}}{1\textup{ foot}} = \frac{64\textup{ inches}}{x\textup{ feet}}$

Cross multiply. The dimensions will cancel and we will be solving for the unknown variable.

12x=64

Divide by 12 on both sides.

$x=\frac{64}{12}$

Reduce the fraction by writing out the factors.

$x=\frac{64}{12} =\frac{4\times 4 \times 4 }{4\times 3 }$

Cancel the four and simplify.

The answer is: $x= \frac{16}{3}$

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Example Question #84 : Converting Measurements

Pecans can be purchased in bulk for $8.50 per pound at Charlie's grocery; the weight of the pecans purchased need not be a whole number of pounds. David has dollars on hand and wants to purchase as many pecans as he can afford. In terms of , how many ounces can he purchase?

Possible Answers:

$\frac{N}{272}$

272N

$\frac{N}{126}$

$\frac{17N} {32}$

$\frac{32N} {17}$

Correct answer:

$\frac{32N} {17}$

Explanation:

David has dollars and can purchase pecans at $8.50, or $8.5 = 8 \frac{1}{2} = \frac{17}{2}$ dollars, per pound. He can purchase

$N \div \frac{17}{2} = N \cdot \frac{2} {17} = \frac{2N} {17}$

pounds of pecans for dollars.

Since 16 ounces are equal to one pound, this converts to

$\frac{2N} {17} \cdot 16 = \frac{32N} {17}$

ounces of pecans.

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Example Question #83 : Converting Measurements

Danny drove miles in two hours. What was his average speed in feet per second?

Possible Answers:

$\frac{11}{60} N$

$\frac{15}{11} N$

None of the other responses gives a correct answer.

$\frac{11}{15} N$

$\frac{60}{11} N$

Correct answer:

$\frac{11}{15} N$

Explanation:

One mile is equal to 5,280 feet; one hour is equal to 3,600 seconds.

Danny drove miles, which is equal to 5,280N feet, in two hours, or $2 \cdot 3,600 = 7,200$ seconds. divide the distance by the time to get the rate:

$\frac{5,280N}{7,200} = \frac{5,280}{7,200} N = \frac{5,280 \div 480 }{7,200\div 480 } N =\frac{11}{15} N$ feet per second.

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Example Question #1311 : Linear Equations

A board comprises four segments, each of length 40 centimeters. What is the total length of the board in meters?

Possible Answers:

0.1 meters

0.16 meters

0.01 meters

1 meter

1.6 meters

Correct answer:

1.6 meters

Explanation:

$40 \times 4 = 160$ , so the board is 160 centimeters long. One meter is equal to 160 centimeters, so divide by 100 to convert to meters:

$160 \div 100 =1.6$ meters, the correct choice.

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Example Question #1312 : Linear Equations

One inch converts to 2.54 centimeters. Quinn is 5 feet, 6 inches tall. Which of the following is the closest to his height in meters?

Possible Answers:

1.8 meters

1.6 meters

2 meters

1.9 meters

1.7 meters

Correct answer:

1.7 meters

Explanation:

5 feet, 6 inches converts to $5 \times 12 + 6 = 60+6 = 66$ inches. Multiply this by conversion factor 2.54 to convert to centimeters:

$66 \times 2.54 = 167.64$ centimeters.

One meter converts to 100 centimeters, so divide by 100:

$167.64 \div 100 = 1.6764$ meters.

This rounds to 1.7 meters, making this the correct choice.

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Example Question #1313 : Linear Equations

Four of the following measurements are equal to one another. Which choice does not refer to the same length as the other four?

Possible Answers:

7,000,000 millimeters

700,000 centimeters

700 decimeters

7 kilometers

7,000 meters

Correct answer:

700 decimeters

Explanation:

One kilometer converts to 1,000 meters, so 7 kilometers converts to

$7 \times 1,000 = 7,000$ meters.

One meter converts to 10 decimeters, 100 centimeters, and 1,000 millimeters, so 7,000 meters converts to

$7,000 \times 10 = 70,000$ decimeters,

$7,000 \times 100 = 700,000$ centimeters,

and

$7,000 \times 1,000 = 7,000,000$ millimeters.

Therefore, 7 kilometers, 7,000 meters, 700,000 centimeters, and 7,000,000 millimeters refer to the same length. This length is equal to 70,000 decimeters, not 700 decimeters, 700 decimeters is the "odd man out" and is the correct choice.

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #79 : Converting Measurements

Example Question #80 : Converting Measurements

Example Question #81 : Converting Measurements

Example Question #81 : Converting Measurements

Example Question #82 : Converting Measurements

Example Question #84 : Converting Measurements

Example Question #83 : Converting Measurements

Example Question #1311 : Linear Equations

Example Question #1312 : Linear Equations

Example Question #1313 : Linear Equations

All Algebra 1 Resources

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