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SAT Mathematics : Solving Word Problems with Multiple Unit Conversions

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Example Question #1 : Solving Word Problems With Multiple Unit Conversions

Nancy is visiting her grandmother who lives 200km $\displaystyle 200km$ from her home. Her car’s tank has a full tank ( $\displaystyle 20$ liters) at the beginning of her drive and uses $\displaystyle 1$ liter to drive $\displaystyle 6$ kilometers. How many liters will she need to refill to reach her grandmother’s house with $\displaystyle 0$ liters left in the tank?

Possible Answers:

$\displaystyle 20$ liters

She will not need to refill.

13.3 $\displaystyle 13.3$ liters

9.8 $\displaystyle 9.8$ liters

Correct answer:

13.3 $\displaystyle 13.3$ liters

Explanation:

The correct answer is 13.3 $\displaystyle 13.3$ liters. $\frac{6\, kilometers}{1\, liter}*20\, liters=120km$ $\displaystyle \frac{6\, kilometers}{1\, liter}*20\, liters=120km$ . $\displaystyle 200-120=80$ . $\frac{1\, liter}{6\, kilometers}*80\, kilometers=13.3\, liters$ $\displaystyle \frac{1\, liter}{6\, kilometers}*80\, kilometers=13.3\, liters$ .

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Example Question #2 : Solving Word Problems With Multiple Unit Conversions

A future pharmacist is unsure what dose they should fill to ensure a patient takes a $\displaystyle 35$ -mg tablet $\displaystyle 4$ times a day for one whole week. What is the total dosage they should prescribe?

Possible Answers:

200mg $\displaystyle 200mg$

980mg $\displaystyle 980mg$

1300mg $\displaystyle 1300mg$

2000mg $\displaystyle 2000mg$

Correct answer:

980mg $\displaystyle 980mg$

Explanation:

The correct answer is 980 $\displaystyle 980$ mg. $\frac{35\, mg}{1\, tablet}*\frac{4\, tablet}{1\, day}*\frac{7\, days}{1\, week}=980mg$ $\displaystyle \frac{35\, mg}{1\, tablet}*\frac{4\, tablet}{1\, day}*\frac{7\, days}{1\, week}=980mg$ .

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Example Question #3 : Solving Word Problems With Multiple Unit Conversions

A patient is prescribed 24mg $\displaystyle 24mg$ of a certain drug per day and is allowed to refill his prescription twice. If there are $\displaystyle 18$ tablets in a prescription, and each tablet has 16mg $\displaystyle 16mg$ , how many doses are in the $\displaystyle 3$ prescriptions (original + $\displaystyle 2$ refills)?

Possible Answers:

$\displaystyle 27$ doses

$\displaystyle 41$ doses

$\displaystyle 62$ doses

$\displaystyle 81$ doses

Correct answer:

$\displaystyle 81$ doses

Explanation:

$3\, prescriptions*\frac{18\, tablets}{1\, prescription}*\frac{24\, mg}{1\, tablet}*\frac{1\, dose}{16\, mg}=81\, doses$ $\displaystyle 3\, prescriptions*\frac{18\, tablets}{1\, prescription}*\frac{24\, mg}{1\, tablet}*\frac{1\, dose}{16\, mg}=81\, doses$

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Example Question #4 : Solving Word Problems With Multiple Unit Conversions

A fruit farm produces strawberries and employs $\displaystyle 7$ workers. Each worker can pick $\displaystyle 3$ pounds of berries per hour and work an $\displaystyle 8$ -hour shift. If each pound of strawberries can be sold for $\$4$ $\displaystyle \$4$ , how much money does the farm make every day?

Possible Answers:

$\$168$ $\displaystyle \$168$

$\$336$ $\displaystyle \$336$

$\$672$ $\displaystyle \$672$

$\$224$ $\displaystyle \$224$

Correct answer:

$\$672$ $\displaystyle \$672$

Explanation:

The key here is to ensure your units cancel out. $\frac{3\, lbs}{1\, worker*1\, hr}*\frac{4\, dollars}{1\, lb}*\frac{8\, hrs*7\, workers}{1\, day\, of\, labor}=\$672$ $\displaystyle \frac{3\, lbs}{1\, worker*1\, hr}*\frac{4\, dollars}{1\, lb}*\frac{8\, hrs*7\, workers}{1\, day\, of\, labor}=\$672$ .

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Example Question #5 : Solving Word Problems With Multiple Unit Conversions

A record has a radius of $\displaystyle 5$ inches with the needle resting on the outer circumference of the record. If the record rotates at a speed of $\frac{\pi }{4}$ $\displaystyle \frac{\pi }{4}$ radians/sec and it takes $\displaystyle 3$ minutes to play a full song, how inches of track have been covered by the end of the song?

Possible Answers:

112.5 $\displaystyle 112.5$

353.3 $\displaystyle 353.3$

1776 $\displaystyle 1776$

706.5 $\displaystyle 706.5$

Correct answer:

706.5 $\displaystyle 706.5$

Explanation:

Circumference $=2\pi r=10\pi$ $\displaystyle =2\pi r=10\pi$ inches. The key here is to ensure your units cancel out. $\frac{10\pi \, inches}{1\, revolution}*\frac{1\, revolution}{2\pi \, radians}*\frac{\frac{\pi }{4}\, radians}{1\, second}*\frac{60\, seconds}{1\, minute}*3\, minutes=706.5$ $\displaystyle \frac{10\pi \, inches}{1\, revolution}*\frac{1\, revolution}{2\pi \, radians}*\frac{\frac{\pi }{4}\, radians}{1\, second}*\frac{60\, seconds}{1\, minute}*3\, minutes=706.5$ inch.

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Example Question #1 : Solving Word Problems With Multiple Unit Conversions

A student was traveling $\displaystyle 50$ miles per hour. What is the student’s speed in feet per second?

Possible Answers:

4400 $\displaystyle 4400$

80.8 $\displaystyle 80.8$

73.3 $\displaystyle 73.3$

728 $\displaystyle 728$

Correct answer:

73.3 $\displaystyle 73.3$

Explanation:

$\frac{50\, mi}{1\, hr}*\frac{1\, hr}{3600\, sec}*\frac{5280\, ft}{1\, mi}=73.3\, ft/sec$ $\displaystyle \frac{50\, mi}{1\, hr}*\frac{1\, hr}{3600\, sec}*\frac{5280\, ft}{1\, mi}=73.3\, ft/sec$

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Example Question #1 : Solving Word Problems With Multiple Unit Conversions

Convert $9\, ft^{3}$ $\displaystyle 9\, ft^{3}$ to $yd^{3}$ $\displaystyle yd^{3}$ .

Possible Answers:

$\displaystyle 1$

0.33 $\displaystyle 0.33$

$\displaystyle 3$

0.25 $\displaystyle 0.25$

Correct answer:

0.33 $\displaystyle 0.33$

Explanation:

$9\, ft^{3}*\left ( \frac{1\, yd}{3\, ft} \right )^{3}=9\, ft^{3}*\left ( \frac{1\, yd^{3}}{27\, ft^{3}} \right )=0.33\, yd^{3}$ $\displaystyle 9\, ft^{3}*\left ( \frac{1\, yd}{3\, ft} \right )^{3}=9\, ft^{3}*\left ( \frac{1\, yd^{3}}{27\, ft^{3}} \right )=0.33\, yd^{3}$

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Example Question #3 : Solving Word Problems With Multiple Unit Conversions

The local track is 400 $\displaystyle 400$ yds. How many laps would a student need to cover to run $\displaystyle 3$ miles?

Possible Answers:

8.8 $\displaystyle 8.8$

17.6 $\displaystyle 17.6$

4.4 $\displaystyle 4.4$

13.2 $\displaystyle 13.2$

Correct answer:

13.2 $\displaystyle 13.2$

Explanation:

$\frac{1\, lap}{400\, yds}*\frac{1\, yd}{3\, ft}*\frac{5280\, ft}{1\, mi}*3\, miles=13.2\, laps$ $\displaystyle \frac{1\, lap}{400\, yds}*\frac{1\, yd}{3\, ft}*\frac{5280\, ft}{1\, mi}*3\, miles=13.2\, laps$

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Example Question #3 : Solving Word Problems

A blood bank was hoping to collect $\displaystyle 50$ gallons of blood over the holiday season. If 250 $\displaystyle 250$ people came in and donated a pint of blood each, how many gallons were they short?

Possible Answers:

They met their goal

$\displaystyle 19$

$\displaystyle 9$

$\displaystyle 31$

Correct answer:

$\displaystyle 19$

Explanation:

$250\, pints*\frac{1\, qt}{2\, pints}*\frac{1\, gallon}{4\, qt}=31.25$ $\displaystyle 250\, pints*\frac{1\, qt}{2\, pints}*\frac{1\, gallon}{4\, qt}=31.25$ gallons collected. $\displaystyle 50-31.25=18.75$ gallons short.

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Example Question #1 : Solving Word Problems With Multiple Unit Conversions

How many seconds are in a week?

Possible Answers:

10,080 $\displaystyle 10,080$

86,400 $\displaystyle 86,400$

604,800 $\displaystyle 604,800$

$\displaystyle 36,288,000$

Correct answer:

604,800 $\displaystyle 604,800$

Explanation:

$1\, week*\frac{7\, days}{1\, week}*\frac{24\, hr}{1\, day}*\frac{60\, min}{1\, hr}*\frac{60\, sec}{1\, min}=604,800$ $\displaystyle 1\, week*\frac{7\, days}{1\, week}*\frac{24\, hr}{1\, day}*\frac{60\, min}{1\, hr}*\frac{60\, sec}{1\, min}=604,800$

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SAT Mathematics : Solving Word Problems with Multiple Unit Conversions

Study concepts, example questions & explanations for SAT Mathematics

All SAT Mathematics Resources

Example Questions

Example Question #1 : Solving Word Problems With Multiple Unit Conversions

Example Question #2 : Solving Word Problems With Multiple Unit Conversions

Example Question #3 : Solving Word Problems With Multiple Unit Conversions

Example Question #4 : Solving Word Problems With Multiple Unit Conversions

Example Question #5 : Solving Word Problems With Multiple Unit Conversions

Example Question #1 : Solving Word Problems With Multiple Unit Conversions

Example Question #1 : Solving Word Problems With Multiple Unit Conversions

Example Question #3 : Solving Word Problems With Multiple Unit Conversions

Example Question #3 : Solving Word Problems

Example Question #1 : Solving Word Problems With Multiple Unit Conversions

All SAT Mathematics Resources

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