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Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries sells for $1.50 and each pound of grapes sells for $2.75. Arun made $130.25 from selling a total of 66 pounds of raspberries and grapes. Determine the number of pounds of raspberries sold and the number of pounds of grapes sold.

Question

Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries sells for 1.50andeachpoundofgrapessellsfor1.50 and each pound of grapes sells for 2.75. Arun made $130.25 from selling a total of 66 pounds of raspberries and grapes. Determine the number of pounds of raspberries sold and the number of pounds of grapes sold.

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Solution

Let's denote the number of pounds of raspberries sold as r r and the number of pounds of grapes sold as g g .

We have two pieces of information:

  1. The total weight of raspberries and grapes sold is 66 pounds.
  2. The total revenue from selling the raspberries and grapes is $130.25.

We can set up the following system of equations based on this information:

  1. r+g=66 r + g = 66
  2. 1.50r+2.75g=130.25 1.50r + 2.75g = 130.25

First, we can solve the first equation for r r :

r=66−g r = 66 - g

Next, we substitute this expression for r r into the second equation:

1.50(66−g)+2.75g=130.25 1.50(66 - g) + 2.75g = 130.25

Now, distribute the 1.50:

99−1.50g+2.75g=130.25 99 - 1.50g + 2.75g = 130.25

Combine like terms:

99+1.25g=130.25 99 + 1.25g = 130.25

Subtract 99 from both sides:

1.25g=31.25 1.25g = 31.25

Divide both sides by 1.25:

g=25 g = 25

Now that we have g g , we can find r r by substituting g g back into the first equation:

r+25=66 r + 25 = 66

Subtract 25 from both sides:

r=41 r = 41

So, Arun sold 41 pounds of raspberries and 25 pounds of grapes.

This problem has been solved

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