Caleb runs a farm stand that sells strawberries and grapes. Yesterday Caleb sold 28 pounds of strawberries and 37 pounds of grapes for a total revenue of $$ \$ 183.50 $$. Today he sold 14 pounds of strawberries and 16 pounds of grapes for a total revenue of $$ \$ 85.50 $$. Determine the price of each pound of strawberries and the price of each pound of grapes. Answer Attempt 1 out of 10 Each pound of strawberries costs $$ \$ \square $$ and each pound of grapes costs $$ \$ \square $$.

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UpStudy AI · Accepted Answer

Let's determine the prices of strawberries and grapes by setting up a system of equations based on Caleb's sales.

Let:
- $$ s $$ = price per pound of strawberries
- $$ g $$ = price per pound of grapes

**From yesterday's sales:**
$$ 28s + 37g = 183.50 \quad \text{(Equation 1)} $$

**From today's sales:**
$$ 14s + 16g = 85.50 \quad \text{(Equation 2)} $$

**Step 1: Eliminate one variable**

To eliminate $$ s $$, multiply Equation 2 by 2:
$$ 28s + 32g = 171.00 \quad \text{(Equation 3)} $$

Subtract Equation 3 from Equation 1:
$$
\begin{align*}
(28s + 37g) - (28s + 32g) &= 183.50 - 171.00 \
5g &= 12.50 \
g &= \frac{12.50}{5} \
g &= 2.50
\end{align*}
$$

**Step 2: Solve for $$ s $$**

Substitute $$ g = 2.50 $$ into Equation 2:
$$
\begin{align*}
14s + 16(2.50) &= 85.50 \
14s + 40 &= 85.50 \
14s &= 45.50 \
s &= \frac{45.50}{14} \
s &= 3.25
\end{align*}
$$

**Conclusion:**
- **Each pound of strawberries costs** $$ \$3.25 $$.
- **Each pound of grapes costs** $$ \$2.50 $$.

**Final Answer:**
Each pound of strawberries costs $3.25 and each pound of grapes costs $2.50.
Each pound of strawberries costs \$3.25 and each pound of grapes costs \$2.50.

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