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Alice has x stamps and Thomas has y stamps, where x and y ar

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sanjoo
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Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   Updated on: 07 Jan 2014, 05:35
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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
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A

Originally posted by sanjoo on 07 Jan 2014, 05:23.
Last edited by Bunuel on 07 Jan 2014, 05:35, edited 2 times in total.
Edited the question.
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   07 Jan 2014, 05:35
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sanjoo wrote:
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


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.
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   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
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   14 Jun 2017, 21:45
sanjoo wrote:
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


Given that
X/Y = 7/3 --------- ( 1 )

( X - Z ) / ( Y + Z ) = 7/8
=> ( X - Z ) ( 3X/7 + Z ) = 7/8 ( from equation 1 )
=> 8X - 8Z = 3X + 7Z
=> 5X = 15Z
=> Z = X/3

Answer : A
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Alice has x stamps and Thomas has y stamps, where x and y are... [#permalink] New post   25 Jun 2018, 17:31
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
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Re: Alice has x stamps and Thomas has y stamps, where x and y are... [#permalink] New post   25 Jun 2018, 19:12
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Carlgrc wrote:
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



X/y=7/3....y=3x/7
Also (x-z)/(y+z)=7/8
8x-8z=7y+7z......8x-7y=15z
Substitute y = 3x/7
So 8x-7*3x/7=15z......8x-3x=15z.....5x=15z
Z=X/3

A
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Re: Alice has x stamps and Thomas has y stamps, where x and y are... [#permalink] New post   25 Jun 2018, 19:41
x/y = 7/3 hence, 7y = 3x

(x-z)/(y+z) = 7/8
8x - 8z = 7y + 7z = 3x + 7z
5x = 15z
z = x/3
so A
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   25 Jun 2018, 19:44
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Carlgrc wrote:
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


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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   12 Jul 2020, 15:50
sanjoo wrote:
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


3x = 7y
And, 8*(x - z) = 7*(y + z)
or, 8x - 8z = 7y + 7z
or, z = 8x - 7y /15 =(8x - 7*3x/7)/15 = 5x/15 = x/3.
A is the answer.
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink] New post   14 Oct 2022, 11:39
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Re: Alice has x stamps and Thomas has y stamps, where x and y ar [#permalink]
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