Math Problem Statement

A restaurant offers delivery for their pizzas and includes the delivery fee in the total price of the pizzas. One customer pays $25 to have 2 pizzas delivered. Another customer pays $58 for 5 pizzas. How many pizzas are delivered to a customer who pays $80? (Hint: How much extra money did the 3 extra pizzas cost? What is the cost per pizza? What is the delivery fee?)

Solution

The problem you uploaded can be broken down as follows:

We have three pieces of information:

  1. A customer pays $25 for 2 pizzas delivered.
  2. Another customer pays $58 for 5 pizzas delivered.
  3. We need to determine how many pizzas a customer receives if they pay $80.

Step 1: Set up equations for both customers.

Let pp be the cost per pizza, and dd be the delivery fee. For each situation:

  • For the first customer:
    2p+d=252p + d = 25

  • For the second customer: 5p+d=585p + d = 58

Step 2: Solve for pp and dd.

Subtract the first equation from the second:

(5p+d)(2p+d)=5825(5p + d) - (2p + d) = 58 - 25 3p=333p = 33 p=11p = 11

Now substitute p=11p = 11 into the first equation: 2(11)+d=252(11) + d = 25 22+d=2522 + d = 25 d=3d = 3

Step 3: Calculate for the $80 payment.

Now that we know the cost per pizza is $11 and the delivery fee is $3, set up the equation for a customer who pays $80: xp+d=80xp + d = 80 Substitute p=11p = 11 and d=3d = 3: 11x+3=8011x + 3 = 80 11x=7711x = 77 x=7x = 7

Answer:

The customer who pays $80 gets 7 pizzas.


Do you want more details on any part of this solution or have any questions?

Here are some related questions for further practice:

  1. If a customer paid $100, how many pizzas would they get?
  2. What would the total cost be for 8 pizzas delivered?
  3. If the delivery fee were increased to $5, how would that affect the number of pizzas a customer gets for $80?
  4. How much would 3 pizzas cost without the delivery fee?
  5. How would the equations change if the price per pizza were different for different customers?

Tip: When you have two variables, solving systems of equations is a great strategy!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

2p + d = 25
5p + d = 58
xp + d = 80

Theorems

System of Linear Equations
Substitution Method

Suitable Grade Level

Grade 8-10