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Algebra 1 : Converting Measurements

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Example Question #1 : Converting Measurements

Harold has a (full) two liter bottle of soda in his refrigerator. He takes it out and pours eight-ounce glasses of soda for himself and each of his three friends that have come over. How many liters of soda are left in the bottle (rounded to two decimal places)?

1 liter = 33.814 fluid ounces

Possible Answers:

1.29L

0.95L

1.05L

0.71L

1.00L

Correct answer:

1.05L

Explanation:

Convert the two liters of soda into ounces.

2 * 33.814 = 67.628

Subtract the four eight-ounce glasses of soda that were poured.

67.628 - (4*8)=35.628

Convert the remaining ounces back into liters.

$35.628 * \frac{1}{33.814} = 1.05$

Alternatively, you could set it up as one equation and solve for , as shown below.

$x = 2 - [(8\times 4)\times\tfrac{1}{33.814}]$

x = 2 - 0.95

x=1.05

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Example Question #2 : Converting Measurements

Convert 60 mph (miles per hour) into fps (feet per second).

Possible Answers:

$50\ fps$

$0.7\ fps$

$41\ fps$

$88\ fps$

$16\ fps$

Correct answer:

$88\ fps$

Explanation:

To replace hours with seconds, you must divide by 3600 (seconds in an hour), and to replace miles with feet you must multiply by 5280 (number of feet in a mile).

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Example Question #2 : Converting Measurements

Edward is driving 225 miles to go home for Christmas vacation. The last time Edward took this trip, he drove miles per hour. How much shorter would Edward's trip be this time if he drives miles per hour?

Possible Answers:

$3\ \textup{hours}$

$1\ \textup{hour}$

$4\ \textup{hours}$

$45\ \textup{minutes}$

$3\ \textup{hours and}\ 45\ \textup{minutes}$

Correct answer:

$45\ \textup{minutes}$

Explanation:

This problem relies on the formula $\textup{distance = rate * time}$ , or d = rt .

Solving for in the case of both Edward's original trip and the trip Edward will take this time will give us the time each trip would take. The difference between these times is the answer.

The distance Edward travels is 225 miles. The rate at which he drives on the first trip is miles per hour. Remember that in writing out equations we can treat the word "per" as a division sign, so we express $60 \textup{ miles per hour}$ as $\frac{60 \ miles}{1 \ hour}$ . Solve for with these numbers in d = rt .

$225 \ miles = (\frac{60 \ miles}{1 \ hour}) * (t \ hours)$

$(225 \ miles) * (\frac{1 \ hour}{60 \ miles}) = (\frac{60 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{60 \ miles})$

$\frac{225}{60} \ hours = t \ hours$

$t = \frac{15}{4} \ hours = 3\tfrac{3}{4} \ hours$

To convert the remainder fraction of an hour into minutes, multiply it by $60 \ minutes \ per \ hour$ .

$\frac{3}{4} \ hours * \frac{60 \ minutes}{1 \ hour} = \frac{180}{4} \ minutes = 45 \ minutes$

So the total time for the original trip is hours and minutes.

Now use the same d = rt equation, but replace the miles per hour with miles per hour for the second trip.

$225 \ miles = (\frac{75 \ miles}{1 \ hour}) * (t \ hours)$

$(225 \ miles) * (\frac{1 \ hour}{75 \ miles}) = (\frac{75 \ miles}{1 \ hour}) * (t \ hours) * (\frac{1 \ hour}{75 \ miles})$

$\frac{225}{75} \ hours = t \ hours$

$t = 3 \ hours$

We now know the trip at miles per hour would be hours long. Subtracting this from the length of the original miles per hour trip gives us the amount of time by which this trip would be shorter than the original.

$(3 \ hours, 45 \ minutes) - (3 \ hours) = 45 \ minutes$

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Example Question #2 : Converting Measurements

Albert is traveling at 70 kilometers per hour, Joseph is moving at 35 meters per second, and Katrina is moving at 1.9 kilometers per minute. Which person is traveling the fastest?

Possible Answers:

Katrina and Albert are tied for the fastest speed.

Katrina

All three individuals are traveling at the same speed.

Albert

Joseph

Correct answer:

Joseph

Explanation:

To compare these three different measurements, we need to convert them so they have the same units. Let's convert all three values into meters per second.

Multiplying 70 km/h by 1000 m/km gives us 70,000 meters per hour, and dividing that value by 3600 (since there are 3600 seconds in an hour) gives us 19.4. So, Albert is traveling at 19.4 meters per second.

We convert Katrina's speed in a similar way, multiplying 1.9 km/minute by 1000 m/km and then dividing by 60 (since there are 60 seconds in a minute). These calculations give us 31.67 m/s.

Since both of these values are slower than Joseph's speed of 35 m/s, Joseph is traveling the fastest.

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Example Question #3 : Converting Measurements

The density of a substance is grams per cubic centimeter. In terms of , what is the mass, in kilograms, of one cubic meter of this substance?

Possible Answers:

$X \; \textrm{kg}$

$1,000,000X \; \textrm{kg}$

$\frac{1,000,000}{X} \; \textrm{kg}$

$\frac{1,000}{X} \; \textrm{kg}$

$1,000X \; \textrm{kg}$

Correct answer:

$1,000X \; \textrm{kg}$

Explanation:

1 meter is equal to 100 centimeters, so 1 cubic meter is equal to $100^{3} = 1,000,000$ cubic centimeters.

1,000,000 cubic centimeters has mass:

$1,000,000 \textrm{\;cm}^{3} \cdot X \frac{\textrm{g}}{\textrm{cm}^{3}} = 1,000,000X \textrm{\; g}$

1,000 grams are in a kilogram, so convert to kilograms by dividing this number by 1,000:

$1,000,000 X \div 1,000 = 1,000 X$

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Example Question #4 : Converting Measurements

Three centimeters on a map represents 45 actual kilometers. In terms of , how many centimeters on the map represent actual kilometers?

Possible Answers:

$\frac{N}{135}$

15N

$\frac{135}{N}$

$\frac{N}{15}$

$\frac{15}{N}$

Correct answer:

$\frac{N}{15}$

Explanation:

Let be the number of map centimeters that represent kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for

$\frac{x}{N} = \frac{3}{45}$

$\frac{x}{N} = \frac{1}{15}$

$\frac{x}{N} \cdot N = \frac{1}{15}\cdot N$

$x = \frac{N}{15}$

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Example Question #5 : Converting Measurements

Three centimeters on a map represents 66 actual kilometers. In terms of , how many centimeters on the map represent actual kilometers?

Possible Answers:

22N

198N

$\frac{N}{22}$

$\frac{198}{N}$

$\frac{22}{N}$

Correct answer:

$\frac{N}{22}$

Explanation:

Let be the number of map centimeters that represent kilometers.

Set up a proportion statement which equates two ratios, each of which compares map centimeters to actual kilometers represented. Then solve for

$\frac{x}{N} = \frac{3}{66}$

$\frac{x}{N} = \frac{1}{22}$

$\frac{x}{N} \cdot N = \frac{1}{22}\cdot N$

$x = \frac{N}{22}$

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Example Question #5 : Converting Measurements

Three centimeters on a map represents 66 actual kilometers. In terms of , how many actual kilometers are represented by centimeters on the map?

Possible Answers:

$\frac{22}{N}$

22N

198N

$\frac{N}{22}$

$\frac{198}{N}$

Correct answer:

22N

Explanation:

Let be the number of actual kilometers represented by map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for .

$\frac{x}{N} = \frac{66}{3}$

$\frac{x}{N} = 22$

$\frac{x}{N} \cdot N = 22 \cdot N$

x = 22N

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Example Question #6 : Converting Measurements

Three centimeters on a map represents 45 actual kilometers. In terms of , how many actual kilometers are represented by centimeters on the map?

Possible Answers:

$\frac{135}{N}$

$\frac{N}{135}$

$\frac{15}{N}$

15N

$\frac{N}{15}$

Correct answer:

15N

Explanation:

Let be the number of actual kilometers represented by map centimeters.

Set up a proportion statement which equates two ratios, each of which compares actual kilometers represented to map centimeters. Then solve for .

$\frac{x}{N} = \frac{45}{3}$

$\frac{x}{N} = 15$

$\frac{x}{N} \cdot N = 15 \cdot N$

x = 15N

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Example Question #5 : Converting Measurements

Daycare currently costs $240 per week. Starting next year, there will be a 15% increase in the cost of daycare. How much will one month of daycare cost?

Assume one month equals four weeks.

Possible Answers:

$\$976$

$\$244$

$\$276$

$\$1104$

Correct answer:

$\$1104$

Explanation:

15% is equal to $\small \frac{15}{100}$ , or 0.15. We can find the amount of the increase by multiplying the original cost by 0.15.

240*0.15=36

The new amount is the sum of the original amount and the increase.

$\small 240+36=276$

This gives us the new cost for one week. The cost for the new month will be four times this amount.

$\small 276*4=1104$

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Algebra 1 : Converting Measurements

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Converting Measurements

Example Question #2 : Converting Measurements

Example Question #2 : Converting Measurements

Example Question #2 : Converting Measurements

Example Question #3 : Converting Measurements

Example Question #4 : Converting Measurements

Example Question #5 : Converting Measurements

Example Question #5 : Converting Measurements

Example Question #6 : Converting Measurements

Example Question #5 : Converting Measurements

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