Ratio question

[gibran]

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?
A. 1 / r+2
B. 1 / 2r + 2
C. 1 / 3r + 2
D. 1 / r+3
E. 1 / 2r+3

[DWarrior]

I = his income
S = amount saved
then amount spent = (I-S)

his next year's amount available to spent will be S(1+r)

We're told that he wants: S(1+r)=(I-S)/2
And we're looking for S/I because that's the fraction of his income he should save

1+r=(I/S-1)/2
2+2r)=I/S-1
3+2r=I/S
S/I=1/(2r+3), E

[tarkumar]

E. 1 / 2r+3

[DMoney]

Originally Posted by DWarrior

I = his income
S = amount saved
then amount spent = (I-S)

his next year's amount available to spent will be S(1+r)

We're told that he wants: S(1+r)=(I-S)/2
And we're looking for S/I because that's the fraction of his income he should save

1+r=(I/S-1)/2
2+2r)=I/S-1
3+2r=I/S
S/I=1/(2r+3), E

Nice approach.. I am curious.. Are you able to extract all pertinent info with ease? If so, how? In these wordy problems, I have issues drawing out all of useful goodness, and end up wasting tons of time using trial and error... Do you have a particular strategy that you like to deplore, or is it that you've done so many, you can just sort of sift through and draw it out... Any advice is appreciated.. thx.

[bose]

imo E

[RamN]

shud be E

[linfongyu]

This was a beast of a problem. I really struggle with translating this word problem into equations... So, DMoney, you're not the only one.

[sonikamadala]

1+ for E

[shailender.bisht]

imo E

[sefb]

Originally Posted by DMoney

Nice approach.. I am curious.. Are you able to extract all pertinent info with ease? If so, how? In these wordy problems, I have issues drawing out all of useful goodness, and end up wasting tons of time using trial and error... Do you have a particular strategy that you like to deplore, or is it that you've done so many, you can just sort of sift through and draw it out... Any advice is appreciated.. thx.

I'd be interested to hear others strategys on how to deal with these types of problems also as I tend to spend too long on these sometimes as well.