Question

A bakery delivers cookies to offices.

• The bakery charges a $5 delivery fee.

• The bakery charges a total of $20.00 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?

y = 1.25x + 5

y = 5x + 1.25

y = 1.25x + 6

y = 5x + 7.5

Answer 1

To determine the equation representing the total charge for a delivery of cookies, we need to analyze the information given.

1. The bakery charges a $5 delivery fee.
2. The cost for 12 cookies is $20.00.
3. The cost for 18 cookies is $27.50.

First, let's define the total charge \(y\) in terms of the number of cookies \(x\). The total charge will consist of a fixed delivery fee plus a variable charge based on the number of cookies.

Since we know the fixed delivery fee is $5, we will represent the total cost as:
\[
y = mx + 5
\]
where \(m\) is the cost per cookie.

Now, we can use the data given to find \(m\):

1. For 12 cookies:
\[
y = 20 \Rightarrow 20 = m(12) + 5
\]
Simplifying this:
\[
20 - 5 = 12m \\
15 = 12m \\
m = \frac{15}{12} = 1.25
\]

2. For 18 cookies:
\[
y = 27.50 \Rightarrow 27.50 = m(18) + 5
\]
Simplifying this:
\[
27.50 - 5 = 18m \\
22.50 = 18m \\
m = \frac{22.50}{18} = 1.25
\]

Both calculations give us \(m = 1.25\).

Now we can write the equation for the total charge:
\[
y = 1.25x + 5
\]

Thus, the correct equation representing the total charge in dollars, \(y\), for a delivery of \(x\) cookies is:
\[
\boxed{y = 1.25x + 5}
\]