Question

11. A customer purchases a stroller and packs of diapers from a store. The table shows the total

cost, in dollars, based on the number of packs of diapers purchased, x.
Packs of Diapers 2
Total Cost (in dollars) $450
6 10
$550 $650
Which function models the relationship between the number of packs of diapers, x, and the
total cost, f(x)?
A f(x) = 25x + 400
B f(x) = 25x + 450
C f(x) = 50x + 400
D f(x) = 50x + 450

Answer 1

Answer: A f(x) = 25x + 400

Answer 2

f(x) = 25x + 400

Explanation:

Here, we want to find the relationship between the number of diaper packs and the total cost

From what we have in the options, we can see a linear relationship;

Since it is a linear relationship, it can be modeled using the equation;

y = mx + b

where m is the slope and b is the y-intercept

From what we have, we can identify the following parts;

where x represents number of diaper packs and f(x) or y represents total cost

The points identifiable are as follows;

(2,450) , (6,550) and (10,650)

The slope will be;

(550-450)/(6-2) = 100/4 = 25

So we have the equation partially as;

y = 25x + b

To get b, we can use any of the points

Let’s use (2,450)

Thus, we have

450 = 25(2) + b

b = 450 - 50

b = 450 - 50

b = 400

So the equation is;

y = 25x + 400

Thus;

f(x) = 25x + 400