A bakery delivers cookies to offices.

Question

*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:

$$y=1.25x+5$$