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You work at a fruit stand that sells apples for $2 per pound, oranges for $5 per pound, and bananas for $3 per pound. Yesterday you sold 60 pounds of fruit and made $180. You sold 10 more pounds of apples than bananas. How many pounds of each kind of fruit did you sell yesterday?

Answer :

Final answer:

To solve this problem, you'll need to set up and solve a system of equations. With algebraic substitution, you find that you sold 28 pounds of apples, 18 pounds of bananas, and 14 pounds of oranges.

Explanation:

The problem can be addressed with algebra. Let's denote the amount of each type of fruit sold as: apples = a, bananas = b, and oranges = o.

From the information given, we have three equations:

  1. a + b + o = 60 pounds (total weight sold)
  2. 2a + 5o + 3b = $180 (total income)
  3. a = b + 10 pounds (10 more pounds of apples than bananas)

From equation (3), we know a= b+10. Substituting this into the first equation gives us (b + 10) + b + o = 60. From this, we have 2b + o = 50. And lets substitute a in the second equation, we get 2(b + 10) + 5o + 3b = 180, this simplifies to 5b + 5o = 160, and further simplifies into b + o = 32.

From the above two equations, we get the following system of linear equations:

  1. 2b + o = 50
  2. b + o = 32

Subtracting the second equation from the first give us b = 18 pounds. Substituting this back into equation (5), we get the weight of o=14 pounds. Finally, substitute b into equation (3), we get the weight of a=18+10=28 pounds.

So, you sold 28 pounds of apples, 14 pounds of oranges, and 18 pounds of bananas yesterday.

Learn more about system of equations here:

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