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# Joanna bought only $0.15 stamps and$0.29 stamps. How many

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Intern
Joined: 17 Nov 2016
Posts: 26
Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many  [#permalink]

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18 Jan 2017, 09:38
Quote:
So when we have equation of a type ax+by=cax+by=c and we know that xx and yy are non-negative integers, there can be multiple solutions possible for xx and yy (eg 5x+6y=605x+6y=60) OR just one combination (eg 15x+29y=44015x+29y=440). Hence in some cases ax+by=cax+by=c is NOT sufficient and in some cases it is sufficient.

Hi. How to figure out if ax+by=c has multiple or single solution of values?
Intern
Joined: 18 Jan 2017
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many  [#permalink]

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18 Jan 2017, 10:24
Ndkms wrote:
Can you please point to the rule that justifies the above statement?

I think we just need to do a trial and error here. In this case for example, there is only one unique set of integer values of x and y that satisfy 15x + 29y = 440
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many  [#permalink]

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23 Feb 2017, 04:45
PROMPT ANALYSIS
Let the number of $0.15 stamp be x and number of$0.29 stamp be y. Total value of stamp = 0.15x +0.29y.

Superset

X can be a nonnegative integer

Translation
In order to find the value of x we need:
1# exact value of x and y
2# two equations with x and y as variable to solve for x and y

Statement analysis
St 1: total value of stamp = 4.40 =0.15x +0.29y. One equation two variable. Since we know that x and y are positive integers. We can say 15x +29y =440: x =(440-29y)/15. The only integer that will satisfy will be x = 10 , y = 10, ANSWER. Hence option b, c, e eliminated.

St 2: x =y. Therefore the total will be 0.44x. We cannot calculate the value of x from this information. INSUFFICIENT.
Option A.
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Re: Joanna bought only $0.15 stamps and$0.29 stamps. How many  [#permalink]

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02 Sep 2018, 20:27
Bunuel wrote:
udaymathapati wrote:
Joanna bought only $0.15 stamps and$0.29 stamps. How many $0.15 stamps did she buy? (1) She bought$4.40 worth of stamps.
(2) She bought an equal number of $0.15 stamps and$0.29 stamps.

Let $$x$$ be the # of $0.15 stamps and $$y$$ the # of$0.29 stamps. Note that $$x$$ and $$y$$ must be an integers. Q: $$x=?$$