2014-08-13 09:00:49

A cellular phone company offers two pricing plans for customers traveling internationally. Either, the customer can pay 49 cents per minute for all calls, or the customer can pay $15 once and 19 cents per minute for calls.  What is the least number of full minutes of calls a customer would have to make for the second option to be cheaper than the first?

(A) 30
(B) 49
(C) 50
(D) 51
(E) 54

The correct answer is D
Explanation: Set up two expressions, and compare them as an inequality. Use m for the minutes of calls a customer would make.

Option 1 can be expressed as 49m
Option 2 can be expressed as 1500 + 19 m (1500 because $15 = 1500 cents)

Let option 2 be the cheaper option, since the question asks for it to be the cheaper option:

1500 + 19m < 49m

Subtract 19 m from both sides to get

1500 < 30m

Divide both sides by 30 to get 50 < m. This means that the customer must make more than 50 minutes of phone calls to make the second option cheaper. Thus, choice D is correct.