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?

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:

a + b + o = 60 pounds (total weight sold)
2a + 5o + 3b = $180 (total income)
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:

2b + o = 50
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.

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