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.

Jane was charged $15/4 = $3.75 per item and George was charged

$39/12 = $3.25 per item, so in addition to the charge per item, there must be an extra charge for each purchase.

We note that George bought 12-4 = 8 more items than Jane and was charged

$39 - $15 = $24 more, or $24/8 = $3 more for each additional item. So if we figure $3 per item, we can find out that extra charge.

Jane paid 4 * $3 = $12 for her 4 items, plus $3 to make her total $15.

George paid 12 * $3 = $36 for his 12 items, plus $3 to make his total $39.

So we can see that if x is the number of items, the store charges

x times $3 plus an extra $3.

Using function notation, we write

f (x) = 3x + 3

and then work out the charge for 22 items:

f (22) = 3 * 22 + 3 = 66 + 3 = 69