Question

A bakery delivers cookies to offices.



*The bakery charges a $5 delivery fee.

*The bakery charges a total of $20 for delivering 12 cookies

*The bakery charges a total of $27.50 for delivering 18 cookies



Which equation represents the total charge in dollars, y, for a delivery of x cookies?

Answer 1

To derive the equation for the total charge \( y \) for a delivery of \( x \) cookies, we first note that there is a fixed delivery fee of $5, and the remaining charge is based on the number of cookies delivered.

From the information provided, we can define the total charge equation as follows:

\[
y = mx + b
\]

where:
- \( y \) is the total charge,
- \( x \) is the number of cookies delivered,
- \( m \) is the cost per cookie,
- \( b \) is the fixed delivery fee ($5).

Given that the delivery fee is $5, we can express that as:

\[
b = 5
\]

Now, we'll calculate the cost per cookie (\( m \)). We have two scenarios based on the deliveries:

1. For 12 cookies, the total charge is $20:
\[
20 = 5 + 12m
\]
Subtracting 5 from both sides gives:
\[
15 = 12m
\]
Dividing by 12:
\[
m = \frac{15}{12} = 1.25 \text{ (cost per cookie)}
\]

2. For 18 cookies, the total charge is $27.50:
\[
27.50 = 5 + 18m
\]
Subtracting 5 from both sides gives:
\[
22.50 = 18m
\]
Dividing by 18:
\[
m = \frac{22.50}{18} = 1.25 \text{ (cost per cookie)}
\]

Both calculations for \( m \) confirm that the cost per cookie is indeed $1.25.

Putting this all together, the equation representing the total charge \( y \) for \( x \) cookies is:

\[
y = 1.25x + 5
\]