SAT Word Problem

Question

Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 − 23d, where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in this equation?

A) Kathy will complete the repairs within 108 days.

B) Kathy starts each week with 108 phones to fix.

C) Kathy repairs phones at a rate of 108 per hour.

D) Kathy repairs phones at a rate of 108 per day.

Answer 1

Remember there are often multiple ways of solving a problem. Do the one that makes sense to you.

Method 1) Recognize this is a linear equation, y = mx + b. Boom. The number next to the variable (m) is your "slope" or rate of change. In this case 23 is that rate of change (homegirl fixes 23 phones per day). The number by itself is the "y-intercept" or the starting point. Here 108 is the starting point (she starts each week with a pile of 108 busted phones). There you go. The answer is B.

Method 2) Unit analysis. You know that the units on the left side of the equation has to be equal to the units on the right side of the equation. You can't have 10 miles + 20 miles = 30 mph. That wouldn't make any sense, right? Therefore, if the problem states that "P is the number of phones," then 108 has to be in "number of phones" and 23d has to be in "number of phones." Look at your answer choices. Only one of them lists 108 with units "number of phones." Answer B.

Furthermore, notice the structure of the answer choices:

A) is your throw-away answer (c'mon son, she's gonna take 108 days to fix some phones? Get outta here)

C) and D) are both rates of change (indicated by the word "per"). If P is not a rate of change, 108 can't be.

It's often possible to use process of elimination to figure these things out. Practice practice practice :)