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 find the equation representing the total charge in dollars, \( y \), for a delivery of \( x \) cookies, we first need to determine the cost per cookie.

1. The **fixed delivery fee** is $5.
2. Thus, the equation can be represented as:
\[
y = mx + 5
\]
where \( m \) is the cost per cookie and \( x \) is the number of cookies.

3. From the problem, we have two scenarios:
- For 12 cookies, the total cost is $20.
- For 18 cookies, the total cost is $27.50.

We can set up two equations based on these conditions:

**For 12 cookies:**
\[
20 = 12m + 5
\]
Simplifying this gives:
\[
20 - 5 = 12m \implies 15 = 12m \implies m = \frac{15}{12} = 1.25
\]

**For 18 cookies:**
\[
27.50 = 18m + 5
\]
Simplifying this gives:
\[
27.50 - 5 = 18m \implies 22.50 = 18m \implies m = \frac{22.50}{18} = 1.25
\]

Since both calculations yield \( m = 1.25 \), we can confirm that the cost per cookie is indeed $1.25.

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

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