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

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Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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Updated on: 07 Jan 2014, 05:35
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45% (medium)

Question Stats:

73% (02:18) correct 27% (03:53) wrong based on 146 sessions

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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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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]

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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: $$8x-3x=(7y+15z)-7y$$ --> $$5x=15z$$ --> $$z=\frac{x}{3}$$.

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Re: Alice has x stamps and Thomas has y stamps, where x and y ar  [#permalink]

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06 Oct 2015, 03:49
1
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]

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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

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Joined: 08 Sep 2017
Posts: 65
Alice has x stamps and Thomas has y stamps, where x and y are...  [#permalink]

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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]

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25 Jun 2018, 19:12
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]

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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]

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25 Jun 2018, 19:44
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 &nbs [#permalink] 25 Jun 2018, 19:44
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