Question

Chang will choose between two restaurants to purchase pizzas for his party. The first restaurant charges a delivery fee of $2 for the entire purchase and $10 per pizza. The second restaurant charges a delivery fee of $5 for the entire purchase and $9 per pizza.
Let x be the number of pizzas purchased.
(a)
For each restaurant, write an expression for the total charge of purchasing x pizzas (with delivery).
Total charge from the first restaurant (in dollars)
Total charge from the second restaurant (in dollars)
(b)
Write an equation to show when the total charge (with delivery) would be the same for each restaurant.

Answer 1

(a) Let's define the total charge for each restaurant based on their pricing structures.

**First Restaurant:**
- Delivery fee: $2
- Cost per pizza: $10
- For \( x \) pizzas, the total charge can be expressed as:
\[
\text{Total charge from the first restaurant} = 2 + 10x
\]

**Second Restaurant:**
- Delivery fee: $5
- Cost per pizza: $9
- For \( x \) pizzas, the total charge can be expressed as:
\[
\text{Total charge from the second restaurant} = 5 + 9x
\]

(b) To find when the total charge from both restaurants is the same, we can set the two expressions equal to each other:
\[
2 + 10x = 5 + 9x
\]

This equation can be solved to find the value of \( x \) when the charges are equal.