SOLUTION: A shopper buys 3 oranges and 5 lemons for $10.26, while a second shopper buys 4 lemons and 6 oranges for $11.16. What is the price of each fruit? I got 3x+5y=10.26 and 4x+6y=11.

Question 476530: A shopper buys 3 oranges and 5 lemons for $10.26, while a second shopper buys 4 lemons and 6 oranges for $11.16. What is the price of each fruit?
I got 3x+5y=10.26 and 4x+6y=11.16
I gave the answer of x=2.88 y=.324 but i was wrong.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Here's a hint for future problems: use a letter for the variables that makes sense. In this problem instead of using x and y (easily confused) use O for oranges (that's letter O, not zero) and use L for lemons. Now write your equations.
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For the three oranges and 5 lemons you get:
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3*O + 5*L = 10.26
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So far, no problem.
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For the 4 lemons and 6 oranges you get:
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6*O + 4*L = 11.16
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Notice the difference in the second equation. You got the lemons and oranges reversed in order when you wrote 4x + 6y = 11.16.
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Now you have the two equations:
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3*O + 5*L = 10.26
6*O + 4*L = 11.16
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Multiply the top equation (both sides and all terms) by 2 to get:
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6*O + 10*L = 20.52 <--- First equation doubled
6*0 + 4*L = 11.16 <--- Second equation unchanged
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Now subtract the two equations vertically and the answer becomes:
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6*L = 9.36
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Solve for the price of lemons by dividing by 6 to get:
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L = 1.56
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Now let's return to the second equation and substitute 1.56 for L. This equation then becomes:
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6*O + (4*1.56) = 11.16
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Multiply the terms in the parentheses and the equation becomes:
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6*O + 6.24 = 11.16
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Subtract 6.24 from both sides and you have:
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6*O = 4.92
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Divide both sides by 6 to get:
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O = 0.82
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So oranges are 82 cents each and lemons are $1.56 each.
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Hope this helped you out a little bit. You obviously know what you are doing, but just made a simple mistake.

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