Question

Write a two-variable equation to represent this situation. Be sure to define the variables
you use in your equation.

Answer 1

Certainly! To create a two-variable equation, we first need to establish a context. Let's consider a scenario involving the sale of two types of items: apples and oranges.

**Scenario:** A fruit shop sells apples and oranges. The shop sells apples for $3 each and oranges for $2 each. Last week, the shop sold a total of 50 fruits (apples and oranges combined), and the total revenue from these sales was $120.

**Define the variables:**
- Let \( x \) represent the number of apples sold.
- Let \( y \) represent the number of oranges sold.

**Constructing the equations:**

1. The first equation represents the total number of fruits sold:
\[
x + y = 50
\]

2. The second equation represents the total revenue from sales:
\[
3x + 2y = 120
\]

So, the two-variable equations that represent this situation are:
\[
\begin{align*}
1. & \quad x + y = 50 \\
2. & \quad 3x + 2y = 120
\end{align*}
\]

These equations can now be used to analyze the sales of apples and oranges at the shop.