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.

Answer 1

f(x) = 3x + 3; f(22) = 69 is the answer

Use the two points given: (4, 15) and (12, 39)

Find the slope: m =

Δy

Δx

=

39 − 15

12 − 4

=

24

8

= 3

Find the y-intercept: y = mx + b, y = 3x + b, 15 = 3(4) + b, 15 = 12 + b, 3 = b

Then substitute m and b into y= mx + b, y = 3x + 3 or f(x) = 3x + 3

Then evaluate, f(22) = 3(22) + 3 = 69

Answer 2

If you spent $33 you would have bought 10 items. $33/$3.30=10

$15/4 items=$3.75 per item
$39/12 items= $3.25 per item

Every $6 the price goes up by 5 cents I believe.