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Algebra 1 : Linear Equations

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Example Questions

Example Question #1321 : Linear Equations

A gasoline tank holds quarts. If gasoline costs $2.10 per gallon, then how many dollars, in terms of , does it cost to fill the tank, assuming it started out empty?

Possible Answers:

8.4N

1.05N

4.2N

0.525N

Correct answer:

0.525N

Explanation:

One gallon is equal to four quarts, so divide the number of quarts by 4 to convert to gallons. This means the tank has capacity $\frac{N}{4}$ gallons. Multiply this by $2.10, the price per gallon:

$\frac{N}{4} \cdot 2.10 = \frac{2.10 N}{4} = 0.525N$

This is the cost in dollars to fill the tank, so this is the correct choice.

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Example Question #81 : Converting Measurements

Convert 2.5 miles to feet.

Possible Answers:

15485

12000

14560

12640

13200

Correct answer:

13200

Explanation:

There are 5280 feet in one mile.

Write the dimensional analysis and multiply by the given distance in miles. We will want to have feet as the designated unit.

$2.5 \textup{ miles }(\frac{5280 \textup{ feet}}{1 \textup{ mile}})= 13200 \textup{ feet}$

The answer is: $13200 \textup{ feet}$

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Example Question #1321 : Algebra 1

Convert thirty centimeters to meters.

Possible Answers:

$3\textup{ m}$

$300\textup{ m}$

$3000\textup{ m}$

$\frac{3}{10}\textup{ m}$

$\frac{3}{100}\textup{ m}$

Correct answer:

$\frac{3}{10}\textup{ m}$

Explanation:

For every centimeter, there is one-hundredth of a meter.

$1 \textup{ cm} = \frac{1}{100} \textup{ m}$

To convert thirty centimeters to meters, simply multiply this number with the conversion factor.

$30 \textup{ cm}\cdot \frac{1\textup{ m}}{100\textup{ cm}} = \frac{3}{10}\textup{ m}$

The answer is: $\frac{3}{10}\textup{ m}$

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Example Question #1322 : Linear Equations

Convert six minutes to seconds.

Possible Answers:

$900\textup{ seconds}$

$3600\textup{ seconds}$

$36\textup{ seconds}$

$360\textup{ seconds}$

$180\textup{ seconds}$

Correct answer:

$360\textup{ seconds}$

Explanation:

There are 60 seconds in a minute. Write the dimensional analysis.

$1\textup{ minute }= 60\textup{ seconds}$

Multiply the given time by the dimensional analysis.

$6\textup{ minutes }(\frac{60\textup{ seconds}}{1\textup{ minute }}) = 360\textup{ seconds}$

Notice that the minute units will cancel, leaving the answer in seconds.

The answer is: $360\textup{ seconds}$

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Example Question #1322 : Algebra 1

Convert 25 minutes to hours.

Possible Answers:

$\frac{2}{5}$

$\frac{1}{4}$

$\frac{3}{8}$

$\frac{5}{12}$

$\frac{4}{9}$

Correct answer:

$\frac{5}{12}$

Explanation:

There are 60 minutes in an hour. Write the dimensional analysis.

$60\textup{ minutes} = 1\textup{ hour}$

Multiply 25 minutes with the dimensional analysis as a fraction of the hours on the numerator and the minutes in the denominator.

$25\textup{ minutes }(\frac{1\textup{ hour}}{60\textup{ minutes}})$

The minutes unit will cancel and leaves us with the hour unit. Multiply and reduce the fraction.

$\frac{25}{60} = \frac{5 \times 5}{12 \times 5} = \frac{5}{12}$

The answer is: $\frac{5}{12}\textup{ hour}$

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Example Question #1323 : Algebra 1

Convert half an inch to feet.

Possible Answers:

$\frac{1}{6}$

$\frac{1}{144}$

$\frac{1}{12}$

$\frac{1}{72}$

$\frac{1}{24}$

Correct answer:

$\frac{1}{24}$

Explanation:

There are 12 inches per foot.

Write the dimensional analysis.

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

Multiply the half inch with the dimensional analysis. Make sure the foot unit is in the numerator and the inches unit is in the denominator so that they can be cancelled.

$\frac{1}{2}\textup{ inch }(\frac{1\textup{ foot}}{12\textup{ inches }}) = \frac{1}{24} \textup{ foot}$

The answer is: $\frac{1}{24}$

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Example Question #95 : Converting Measurements

$\textup{Convert 2 miles to yards.}$

Possible Answers:

3520

3420

1760

1960

2060

Correct answer:

3520

Explanation:

There are $\textup{5280 feet}$ in a mile, and $\textup{3 feet}$ in a yard. Write both dimensional analyses.

$5280\textup{ feet }= 1\textup{ mile}$

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

Multiply the $\textup{2 miles}$ by the conversion factors. Make sure that the mile and the feet units will cancel so that we will get the final unit in yards.

$2\textup{ miles }\left (\frac{5280\textup{ feet }}{1\textup{ mile}} \right )\left (\frac{1\textup{ yard}}{3\textup{ feet }} \right ) = \frac{10560}{3} = 3520\textup{ yards}$

The answer is: $3520\textup{ yards}$

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Example Question #1325 : Linear Equations

$\textup{Convert } \frac{4}{7} \textup{ feet to inches.}$

Possible Answers:

$\frac{1}{21}$

$\frac{7}{48}$

$\frac{16}{7}$

$\frac{48}{7}$

Correct answer:

$\frac{48}{7}$

Explanation:

There are $\textup{12 inches in a foot}$ . Write the dimensional analysis.

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

Multiply the dimensional analysis with the given dimension. Be sure that the feet cancels in order to get the dimension in inches.

Multiply the fractions.

$\frac{4}{7}\textup{ feet } \left (\frac{12\textup{ inches}}{1\textup{ foot}} \right ) = \frac{48}{7}\textup{ inches}$

The answer is: $\frac{48}{7}$

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Example Question #1326 : Linear Equations

Convert 2.35 meters to kilometers.

Possible Answers:

235

2350

0.00235

2.35

0.0235

Correct answer:

0.00235

Explanation:

There are 1000 meters in a kilometer.

Write the equation to express this dimensional analysis.

$1\textup{ kilometer }= 1000\textup{ meters}$

Multiply the dimension with conversion factor. Make sure that the meters unit will cancel.

$2.35\textup{ meters }(\frac{1\textup{ kilometer}}{1000\textup{ meters}})$

Dividing by 1000 is similar to moving the decimal place back three places.

The answer is: $0.00235 \textup{ kilometer}$

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Algebra 1 : Linear Equations

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1321 : Linear Equations

Example Question #81 : Converting Measurements

Example Question #1321 : Algebra 1

Example Question #1322 : Linear Equations

Example Question #1322 : Algebra 1

Example Question #1323 : Algebra 1

Example Question #95 : Converting Measurements

Example Question #1325 : Linear Equations

Example Question #1326 : Linear Equations

All Algebra 1 Resources

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