Aiden runs a farm stand that sells apples and strawberries. Each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries. Write a system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold. Define the variables that you use to write the system.

Let's define the variables as follows:

- Let $ x $ be the number of pounds of apples sold.
- Let $ y $ be the number of pounds of strawberries sold.

### The system of equations:

1. **Total pounds sold**: The total weight of apples and strawberries sold is 35 pounds.
   \[
   x + y = 35
   \]

2. **Total revenue**: Aiden made $80, with apples selling at $2 per pound and strawberries at $3 per pound. This gives the revenue equation:
   \[
   2x + 3y = 80
   \]

### System of equations:
\[
\begin{cases}
x + y = 35 \\
2x + 3y = 80
\end{cases}
\]

This system can be solved to find the values of $ x $ and $ y $, representing the pounds of apples and strawberries sold.

Would you like to see the solution for this system of equations?

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**Relative questions:**
1. What method can be used to solve the system of equations, such as substitution or elimination?
2. How would the system change if apples were sold for $2.50 per pound instead?
3. What happens to the equations if Aiden sold a total of 50 pounds of apples and strawberries instead of 35?
4. How would you graphically represent the system of equations?
5. Can the system be solved using matrices or determinants?

**Tip**: When dealing with systems of equations, substitution is often helpful when one equation can easily be solved for one variable.

Explore how to solve a system of equations to determine the number of pounds of apples and strawberries sold at Aiden's farm stand. With apples at $2 per pound and strawberries at $3 per pound, Aiden sold a total of 35 pounds and made $80. Learn the step-by-step solution to this algebraic problem, ideal for students in Grades 7-9.

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