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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.Todayhesold45poundsofraspberriesand18poundsofgrapesforatotalrevenueof217. 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.

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Solution

Let's define:

R = price per pound of raspberries G = price per pound of grapes

From the problem, we can create two equations based on the information given.

The first equation is from the first day's sales: 44R + 43G = 217

The second equation is from the second day's sales: 45R + 18G = 144

So, the system of equations to solve is:

44R + 43G = 217 45R + 18G = 144

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