SAT Math - Solving Word Problems with Multiple Unit Conversions

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?

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}=$672$ .

How many seconds are in a week?

Explanation

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

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?

liters

She will not need to refill.

Explanation

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

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?

Explanation

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.

How many $\textup{centimeters}$ are in $13\textup { meters?}$

$1\textup,300\textup { centimeters}$

$130\textup { centimeters}$

$1.3\textup{ centimeters}$

$.0013\textup { centimeters}$

$13\textup,000\textup { centimeters}$

Explanation

To solve this problem we can make proportions.

We know that $1\ centimeter= .01\ meters$ and we can use as our unknown.

$\frac{1\ centimeter}{.01\ meter}=\frac{x\ centimeters}{13\ meters}$

Next, we want to cross multiply and divide to isolate the on one side.

$1\ centimeter\times 13\ meters=.01\ meter\times x\ centimeters$

$\frac{1\ centimeter\times 13\ meters}{.01\ meter}= x\ centimeters$

The will cancel and we are left with $1,300\ centimeters$

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

Explanation

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

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

Explanation

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

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)?

doses

Explanation

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

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

Explanation

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

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?