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 attempt 1 out of 2 let \\(\square =\\)

Explanation:

Step1: Define Variables

Let \( x \) be the price (in dollars) of one pound of raspberries, and let \( y \) be the price (in dollars) of one pound of grapes.

Step2: Form Equation for Yesterday

Yesterday, 44 pounds of raspberries and 43 pounds of grapes were sold for a total of $217. The revenue from raspberries is \( 44x \) and from grapes is \( 43y \). So the equation is \( 44x + 43y = 217 \).

Step3: Form Equation for Today

Today, 45 pounds of raspberries and 18 pounds of grapes were sold for a total of $144. The revenue from raspberries is \( 45x \) and from grapes is \( 18y \). So the equation is \( 45x + 18y = 144 \).

Answer:

Let \( x \) = the price (in dollars) of one pound of raspberries, \( y \) = the price (in dollars) of one pound of grapes.
The system of equations is:
\(

$$\begin{cases} 44x + 43y = 217 \\ 45x + 18y = 144 \end{cases}$$

\)