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How are the variables set in this word problem?
A private art collect sold a canvas at a 10% loss during a financial depression. She bought it years later at an auction and sold it to a museum for $37,000 more than the auction price.
If the gallery made a 25% profit and the collector made a 39.5% net profit on her original investment, for what price did she originally bought the picture.
Let x = original price art collector paid
Let y = price paid at gallery auction years later
During depression, she sold to gallery for 0.9*x
When gallery re-sold it for y, it made a 25% profit, so
y = 1.25*(0.9*x) = 1.125*x
When collector finally sold to museum at $37,000 over the auction price she made a 39.5% profit, so
y + 37,000 = 1.395*x, we know y = 1.125*x, substitute for y
1.125*x + 37,000 = 1.395*x
37,000 = (1.395 – 1.125)*x = 0.27*x
x = 137,037.04
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