Question

practice problems 1 a restaurant offers delivery for their pizzas for a fee added to the price of the pizzas. one customer pays $25 to have 2 pizzas delivered. another customer pays $58 to have 5 pizzas delivered. how many pizzas are delivered to a customer who paid $80?

Explanation:

Step1: Find the cost per pizza

Let the cost per pizza be \(x\) and the delivery fee be \(y\).
We have the system of equations:
\(

$$\begin{cases}2x + y=25\\5x + y = 58\end{cases}$$

\)
Subtract the first equation from the second:
\((5x + y)-(2x + y)=58 - 25\)
\(5x + y-2x - y=33\)
\(3x=33\)
\(x = 11\)

Step2: Find the delivery fee

Substitute \(x = 11\) into \(2x + y=25\)
\(2\times11+y=25\)
\(22 + y=25\)
\(y=25 - 22=3\)

Step3: Find the number of pizzas for a \(\$80\) payment

Let the number of pizzas be \(n\).
The equation is \(11n+3 = 80\)
\(11n=80 - 3\)
\(11n=77\)
\(n = 7\)

Answer:

\(7\)