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Question 131057: I am having problems setting up and solving the following word problem, can you help?
1. An art dealer sold 2 artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other art work. Find the actual cost of each artwork.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An art dealer sold 2 artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whereas if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other art work. Find the actual cost of each artwork.
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Let price on 1st artwork be "x"; Let price on 2nd artwork be "y".
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EQUATIONS:
0.25x + 0.10y = 1520
0.10x + 0.25y = 1535
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Rearrange:
25x + 10y = 152000
10x + 25y = 153500
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Multiply 1st by 25 and 2nd by 10 to get:
250x + 100y = 152000*10
250x + 625y = 153500*25
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Subtract 1st from 2nd to get:
625y = 2317500
y = $3708
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Substitute to solve for "x":
250x + 100(3708) = 1520000
250x = 1149200
x = $4596.80
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Cheers,
Stan H.
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