Question 112094
Let the letter "o" represent the cost per orange and the letter "L" represent the cost per
lemon. These costs are in dollars.
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The first shopper buys 3 oranges and therefore spends 3*o on oranges. This shopper also buys 
5 lemons and therefore spends 5*L on lemons. Together these two expenditures add to $10.26
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In equation form this is:
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3*o + 5*L = 10.26
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The second shopper buys 6 oranges and spends 6*o on oranges and buys 4 lemons for a total
of 5*L on lemons. So the total expenditure by this shopper is 6*o plus 4*L and is $11.16
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In equation form this is:
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6*o + 4*L = 11.16
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So the two equations that apply are:
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3*o + 5*L = 10.26 and
6*o + 4*L = 11.16
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We can use variable elimination to solve this pair. Multiply the top equation (both sides
and all terms) by 2. When you do the equation pair becomes:
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6*o + 10*L = 20.52
6*o + 4*L = 11.16
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You now have 6*o in both equations ... so if you subtract the two equations these terms
drop out and when you subtract the vertical columns of these two equations you get:
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6*L = 9.36
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Divide both sides of this equation by 6 and you find that L = $1.56 ... so each lemon 
costs $1.56
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Now you can return to any of the equations and substitute $1.56 for L to find out the
price of the oranges. Let's return to the first equation:
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3*o + 5*L = 10.26
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Replacing L by 1.56 results in:
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3*o + 5*1.56 = 10.26
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Multiplying the 5 times 1.56 reduces the equation to:
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3*o + 7.80 = 10.26
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Subtract 7.80 from both sides to get:
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3*o = 2.46
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And divide both sides by 3 to solve for "o":
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o = 2.46/3 = 0.82
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So each orange costs $0.82 or 82 cents.
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Hope this helps you to understand the problem ...