Question

A store charges their customers based on the number of items that they buy. Jane bought four items and was charged $15 and George bought twelve items and was charged $39. Write a function to model the cost based on the number of items you buy. Then determine how much you bought if you were charged $33.
Responses
A f(x) = 3x + 3; f(10) = 33f(x) = 3x + 3; f(10) = 33
B f(x) = 3x + 3; f(33) = 102f(x) = 3x + 3; f(33) = 102
C f(x) =

x + 3; f(90) = 33f(x) = 1 3 x + 3; f(90) = 33
D f(x) =

x + 3; f(33) = 14f(x) = 1 3 x + 3; f(33) = 14
E f(x) = 3x + 3; f(33) = 94

Answer 1

Let x be the number of items and f(x) the cost. Using points (4,15) and (12,39):

Slope m = (39−15)/(12−4) = 24/8 = 3, so f(x) = 3x + b.
Use (4,15): 15 = 3·4 + b → b = 3.

Thus f(x) = 3x + 3. If f(x) = 33: 3x + 3 = 33 → 3x = 30 → x = 10.

Answer: f(x) = 3x + 3 and you bought 10 items. (Choice A)