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This year Henry will save a certain amount of his income,

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This year Henry will save a certain amount of his income, [#permalink] New post 16 Jan 2006, 10:32
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This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?
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 [#permalink] New post 16 Jan 2006, 13:09
Good question!

Will think on it again tomorow.
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 [#permalink] New post 16 Jan 2006, 13:14
Reqd rate should be = 100/(3+2r)%

Let Z be the Income and X% the reqd. savings rate.

ZX/100 = Savings in 1st Year
Z(100-X)/100 = Spending in 1st Year


ZX/100(1+r) = Amount available for spending next year


2*ZX/100(1+r)=Z(100-X)/100

2X(1+r) = (100-X)

X(2+ 2R+1 ) = 100

X = 100/(3+2r)
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Re: PS word problem [#permalink] New post 17 Jan 2006, 15:09
sperumba wrote:
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?


Total income = x
Saved = y
Spent = x-y

Total available to spend next year = y(1+r)

As per question y(1+r) = (x-y)/2

i.e y = x/(3+2r)

Fraction of total income (y/x) = 1/(3+2r)
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 [#permalink] New post 17 Jan 2006, 15:23
Total income = x(spend) + y(save)

We need to find y/x+y such that

y(r+1) = x/2

y(r+1) = amount available to spend next year
x/2 = half of amount saved this year.

Thus, x = 2y(r+1).

y/( 2y(r+1) + y) = y/y(2r+3) = 1/(2r+3).
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 [#permalink] New post 17 Jan 2006, 17:13
agree with lhotseface & ps_dahlia for providing ans as fraction. I computed the savings as a %. OA pls ?
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 [#permalink] New post 19 Jan 2006, 20:06
Let total savings this year = x
Let total spend this year = y
total income = x+y
Next year available income to spend = x(1+r)
Required to find x/x+y

Savings such that x(1+r) = y/2
hence x/y = 1/2(1+r) = 1/2+2r
hence x/x+y = 1/1+2+2r = 1/3+2r
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Re: PS word problem [#permalink] New post 21 Jan 2006, 18:55
sperumba wrote:
This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?


you mind, if i ask you where did you get this questions from?
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 [#permalink] New post 21 Jan 2006, 20:41
Late but got 1/(3+2r) as well. Good question supermba!
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  [#permalink] 21 Jan 2006, 20:41
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