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Fractions.

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Junior | Next Rank: 30 Posts
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Fractions.

by pm » Wed Jul 06, 2011 7:07 am
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 ?

z = x/3

z = x/2

z = 2x/3

z= 3x/2

z = 3x

Can this question be solved by picking nos?
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by testprepDublin » Wed Jul 06, 2011 7:24 am
x:y = 7:3. We write this as a fraction: x/y = 7/3 => 3x = 7y.

We also have (x-z)/(y+z) = 7/8 => 8x - 8z = 7y +7z => 8x = 7y + 15z.

Taking away the first equation from the second, we get: 5x = 15z => z = x/3.
Deirdre at testprepdublin.com
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