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:
-
The first equation represents the total number of fruits sold: \[ x + y = 50 \]
-
The second equation represents the total revenue from sales: \[ 3x + 2y = 120 \]
So, the two-variable equations that represent this situation are: \[ \begin{align*}
- & \quad x + y = 50 \
- & \quad 3x + 2y = 120 \end{align*} \]
These equations can now be used to analyze the sales of apples and oranges at the shop.