A pizzeria's top-selling pizzas are The Works and The Hawaiian. The Works sells for `$17,` and The Hawaiian sells for `$13.` Ingredient costs for the works are `$450` per week, and ingreading costs for The Hawaiian are `$310` per week. If x represents the number of each type of pizza sold in one week, and the weekly profit from the sale of each type of pizza is the same, what is the values of x ?

Options

A. 30
B. 35
C. 140
D. 145

Explanation

To solve the problem, we need to find the number of each type of pizza sold in one week (denoted as \( x \)) such that the weekly profit from selling The Works and The Hawaiian pizzas is the same.

### Step-by-Step Solution:

1. **Define the Variables:**
- Let \( x \) be the number of each type of pizza sold in one week.
- Selling price of The Works pizza = $17
- Selling price of The Hawaiian pizza = $13
- Ingredient cost for The Works pizza = $450 per week
- Ingredient cost for The Hawaiian pizza = $310 per week

2. **Calculate the Profit for Each Pizza:**
- Profit from The Works pizza:
\[ \text{Profit}_{\text{Works}} = \text{Revenue} - \text{Cost} = (17x - 450) \]
- Profit from The Hawaiian pizza:
\[ \text{Profit}_{\text{Hawaiian}} = \text{Revenue} - \text{Cost} = (13x - 310) \]

3. **Set the Profits Equal:**
Since the weekly profit from the sale of each type of pizza is the same, we can set the two profit equations equal to each other:
\[ 17x - 450 = 13x - 310 \]

4. **Rearrange the Equation:**
- Move all terms involving \( x \) to one side and constant terms to the other side:
\[ 17x - 13x = 450 - 310 \]
- This simplifies to:
\[ 4x = 140 \]

5. **Solve for \( x \):**
- Divide both sides by 4 to find \( x \):
\[ x = \frac{140}{4} = 35 \]

### Final Answer:
The value of \( x \) is \( 35 \).

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