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.

A) f(x) = 3x + 3; f(10) = 33
B) f(x) = 3x + 3; f(33) = 102
C) f(x) = 1/3x + 3; f(90) = 33
D) f(x) = 1/3x + 3; f(33) = 14

Answer 1

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

So a is your final answer.

I might have done some calculations wrong but thank me for effort.

Answer 2

f(x) = 3x + 3; f(10) = 33

Explanation:

Jane bought four items and was charged $15

`(x_1,y_1)=(4,15)`

George bought twelve items and was charged $39

`(x_2,y_2)=(12,39)`

We will use two point slope form :

Formula :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values :

`y-15=(39-15)/(12-4)(x-4)`

`y-15=3(x-4)`

`y-15=3x-12`

`y=3x+3`

So, f(x)=3x+3

Where f(x) is the cost of x items

We are given that you were charged $33.

So,
`33=3x+3`

`30=3x`

`10=x`

So,f(10)=33

So, Option A is true