SAT I Quant : Arithmetic Word Problem


A ferry service offers its customers two price variants. A $30 pass for up to and including 20 one way trips and $1 per one way trip beyond the 20. Or $1.4 for each one way trip for those who are not pass holders. If x is more than 20 and is the number of one way trips that will cost a customer the same in both the variants, what is x?
A. 30
B. 35
C. 40
D. 25
E. 32

Correct Answer : Choice D. x = 25

Explanatory Answer

Variant 1
In the first variant offered by the ferry service, a passenger pays $30 and gets up to 20 one way trips.

For any number of trips above 20, the passenger is charged $1 per one way trip.

x is the number of one way trips made by the passenger, where x is greater than 20.

So, the passenger pays 30 + (x - 20)*1 if he / she opts for the first variant.

Variant 2
In the second variant, a passenger pays $1.4 for every one way trip.

So, the passenger will pay $1.4x for x one way trips.

x is the number of trips made by the passenger that will cost the passenger the same in both the variants.

Therefore, 30 + (x - 20)*1 = 1.4x
or 30 + x - 20 = 1.4x
or 10 = 0.4x

The correct Answer is 25. Choice D.

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