Solving Word Problems with Multiple Unit Conversions - SAT Math

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

The key here is to ensure your units cancel out. $\frac{3, lbs}{1, worker1, hr}\frac{4, dollars}{1, lb}\frac{8, hrs7, workers}{1, day, of, labor}=$672$ .

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

The local track is yds. How many laps would a student need to cover to run miles?

Answer

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

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Question

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

Answer

$250, pints\frac{1, qt}{2, pints}\frac{1, gallon}{4, qt}=31.25$ gallons collected. gallons short.

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Question

How many seconds are in a week?

Answer

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

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