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# In the first year, someone spent part of his income and

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Director
Joined: 01 Feb 2003
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In the first year, someone spent part of his income and [#permalink]  16 Jun 2005, 21:03
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In the first year, someone spent part of his income and saved the others at the rate r, that is, in the second year, each dollar he saved became 1+r dollar. He has no income in the second year and spends the money he saved in the last year, which is 1/2 of the money spent in the last year. The money he saved in the last year is what fraction of his total income, in terms of r?
VP
Joined: 30 Sep 2004
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x = income saved and y = income spend.

next year he will spend => x(1+r)

In terms of r, what fraction of his income should Henry save this year so that next year the amt he was available to spend will be equal to half the amt that he spends this year?

y/2=x(1+r) => y=2x+2xr insert in x/y+x => x/(2x+2xr+x) => 1/(3+2r)
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Senior Manager
Joined: 30 May 2005
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christoph wrote:
x = income saved and y = income spend.

next year he will spend => x(1+r)

In terms of r, what fraction of his income should Henry save this year so that next year the amt he was available to spend will be equal to half the amt that he spends this year?

y/2=x(1+r) => y=2x+2xr insert in x/y+x => x/(2x+2xr+x) => 1/(3+2r)

please Christoph can you explain what you are doing from y/2=x(1+r) => y=2x+2xr insert in x/y+x => x/(2x+2xr+x) => 1/(3+2r)
thanks
Senior Manager
Joined: 30 May 2005
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mandy wrote:
please Christoph can you explain what you are doing from y/2=x(1+r) => y=2x+2xr insert in x/y+x => x/(2x+2xr+x) => 1/(3+2r)
thanks

Mandy,

In his assumption, x is the money he saved in the first year and y is the money he spent in the first year. So the total money he earned in the first year is x+y

The question says

Quote:
The money he saved in the last year is what fraction of his total income, in terms of r

This means that the fraction needed is x/(x+y)

This has 2 variables. So you solve for y in terms of x and r based on the question and the replace y with that value in the above fraction.

Does this help?
Senior Manager
Joined: 30 May 2005
Posts: 281
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AJB77 wrote:
mandy wrote:
please Christoph can you explain what you are doing from y/2=x(1+r) => y=2x+2xr insert in x/y+x => x/(2x+2xr+x) => 1/(3+2r)
thanks

Mandy,

In his assumption, x is the money he saved in the first year and y is the money he spent in the first year. So the total money he earned in the first year is x+y

The question says

Quote:
The money he saved in the last year is what fraction of his total income, in terms of r

Thanks AJB 77 ! great explanation
a small question plz how do you get this y/2=x(1+r)

This means that the fraction needed is x/(x+y)

This has 2 variables. So you solve for y in terms of x and r based on the question and the replace y with that value in the above fraction.

Does this help?
Senior Manager
Joined: 30 May 2005
Posts: 374
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Kudos [?]: 7 [0], given: 0

Mandy,

x is the money he saved last year. Thanks to the interest, it has now become x(1+r) as stated in the problem.

The problem states - "spends the money he saved in the last year, which is 1/2 of the money spent in the last year"

The first part is x(1+r), the second part is y/2

So x(1+r) = y/2
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