\begin{tabular}{l} Last year for his birthday party, Rory ordered 5 pizzas and 8 \ pounds of wings for $$ \$ 102 $$. This year, he ordered 12 pizzas and 8 \ pounds of wings and it cost $$ \$ 144 $$. \ How much is a single pizza and one pound of wings? \ ( A. A pizza costs $$ \$ 10 $$ and a pound of wings costs $$ \$ 7 $$. \ B. A pizza costs $$ \$ 6 $$ and a pound of wings costs $$ \$ 9 $$. \ C. A pizza costs $$ \$ 5 $$ and a pound of wings costs $$ \$ 10 $$. \ D. A pizza costs $$ \$ 10 $$ and a pound of wings costs $$ \$ 7 $$. \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

To determine the cost of a single pizza and one pound of wings, let's set up a system of equations based on the information provided.

Let:
- $$ p $$ = cost of one pizza
- $$ w $$ = cost of one pound of wings

From **last year's** order:
$$ 5p + 8w = 102 \quad \text{(Equation 1)} $$

From **this year's** order:
$$ 12p + 8w = 144 \quad \text{(Equation 2)} $$

**Step 1: Subtract Equation 1 from Equation 2**
$$
(12p + 8w) - (5p + 8w) = 144 - 102
$$
$$
7p = 42
$$
$$
p = 6
$$

**Step 2: Substitute $$ p = 6 $$ into Equation 1 to find $$ w $$**
$$
5(6) + 8w = 102
$$
$$
30 + 8w = 102
$$
$$
8w = 72
$$
$$
w = 9
$$

**Conclusion:**
- **One pizza costs \$6.**
- **One pound of wings costs \$9.**

**Answer:**  
**B. A pizza costs $6 and a pound of wings costs $9.**
A pizza costs \$6 and a pound of wings costs \$9.

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