Brayden runs a farm stand that sells raspberries and grapes. Yesterday Brayden sold 44 pounds of raspberries and 43 pounds of grapes for a total revenue of $217. Today he sold 45 pounds of raspberries and 18 pounds of grapes for a total revenue of $144. Write a system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes. Define the variables that you use to write the system.

Question

Brayden runs a farm stand that sells raspberries and grapes. Yesterday Brayden sold 44 pounds of raspberries and 43 pounds of grapes for a total revenue of $217. Today he sold 45 pounds of raspberries and 18 pounds of grapes for a total revenue of $144. Write a system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes. Define the variables that you use to write the system.

Answer 1

Let $x$ be the price of each pound of raspberries and $y$ be the price of each pound of grapes.

The first equation can be formed using the information given in the first sentence: $44x + 43y = 217$.

The second equation can be formed using the information given in the second sentence: $45x + 18y = 144$.

So, the system of equations is:
$\begin{cases} 44x + 43y = 217 \\ 45x + 18y = 144 \end{cases}$.