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19 Nov 2009, 06:46
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The price of a house decreased by \(x\%\) from 1998 to 1999 and increased by \(y\%\) from 1999 to 2000. If the house cost \(M\) dollars in 2000, how much did it cost in 1998?
A. \(100 * \frac{\frac{M}{1 + x}}{1 - y}\)
B. \(\frac{\frac{M}{1 + \frac{x}{100}}}{1 - \frac{y}{100}}\)
C. \(\frac{M}{1 + \frac{x}{100} - \frac{y}{100}}\)
D. \(\frac{\frac{10,000M}{100 + y}}{100 - x}\)
E. \(\frac{\frac{10,000M}{100 + x}}{100 - y}\)
A. \(100 * \frac{\frac{M}{1 + x}}{1 - y}\)
B. \(\frac{\frac{M}{1 + \frac{x}{100}}}{1 - \frac{y}{100}}\)
C. \(\frac{M}{1 + \frac{x}{100} - \frac{y}{100}}\)
D. \(\frac{\frac{10,000M}{100 + y}}{100 - x}\)
E. \(\frac{\frac{10,000M}{100 + x}}{100 - y}\)
Denote \(P\) as the price of the house in 1998. We know that \(M = P(1 - \frac{x}{100})(1 + \frac{y}{100})\) . From this equation \(P = \frac{\frac{M}{1 - \frac{x}{100}}}{1 + \frac{y}{100}}\) or \(\frac{\frac{10,000M}{100 + y}}{100 - x}\) .
Is there something wrong in the solution or I'm misreading it?
Say \(X={1 - \frac{x}{100}}\) and \(Y={1 - \frac{y}{100}}\)
If I rewrite the middle step \(M=P(X)(Y)\) => \(P=\frac{M}{XY}\)
=> some representation of \(\frac{10,000M}{(100 + y)(100 - x)}\)
Is there something wrong in the solution or I'm misreading it?
Say \(X={1 - \frac{x}{100}}\) and \(Y={1 - \frac{y}{100}}\)
If I rewrite the middle step \(M=P(X)(Y)\) => \(P=\frac{M}{XY}\)
=> some representation of \(\frac{10,000M}{(100 + y)(100 - x)}\)
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14 Jan 2011, 13:28
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gmattokyo, I had the same question as you did, but after your comment I realized the solution as well 
