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27%
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Alice has x stamps and Thomas has y stamps, where x and y are positive integers. The ratio of x to y is 7 to 3. If Alice gives Thomas z stamps, where z is a positive integer and z < x, and no other changes take place in the numbers of stamps that Alice and Thomas have, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8. Which of the following equations correctly describes z in terms of x?
A. z = x/3
B. z = x/2
C. z = 2x/3
D. z = 3x/2
E. z = 3x
A. z = x/3
B. z = x/2
C. z = 2x/3
D. z = 3x/2
E. z = 3x
07 Jan 2014, 05:35
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sanjoo
The ratio of x to y is 7 to 3 --> \(\frac{x}{y}= \frac{7}{3}\) --> \(3x=7y\);
If Alice gives Thomas z stamps, then the ratio of the number of stamps that Alice has to the number of stamps that Thomas has will become 7 to 8 --> \(\frac{x-z}{y+z} = \frac{7}{8}\) --> \(8x-8z=7y+7z\) --> \(8x=7y+15z\).
Subtract the first equation from the second: \(8x-3x=(7y+15z)-7y\) --> \(5x=15z\) --> \(z=\frac{x}{3}\).
Answer: A.
General Discussion
06 Oct 2015, 03:49
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Ratio of x:y = 7 : 3
\(x/y=7/3\) or \(3x=7y\) (i)
After Alice gives Thomas z stamps, ratio of the number of stamps = 7 : 8
\(x−z/y+z=7/8\)
Or \(8x−8z=7y+7z\)
\(8x=7y+15z.\) (ii)
On performing (ii) - (i), \(5x=15z\)
Or \(z=x/3\)
Option A
\(x/y=7/3\) or \(3x=7y\) (i)
After Alice gives Thomas z stamps, ratio of the number of stamps = 7 : 8
\(x−z/y+z=7/8\)
Or \(8x−8z=7y+7z\)
\(8x=7y+15z.\) (ii)
On performing (ii) - (i), \(5x=15z\)
Or \(z=x/3\)
Option A
