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:
- 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.
Learn more about system of equations here:
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