kskumar wrote:
avigutman can you please explain this ques?
how we can reason from the stem of the question?
kskumar let me know if this helps:
This year Henry will save a certain amount of his income, and he will spend the rest. Set up a 3-way ratio for this year (I know a ratio is a good idea because I glanced at the answer choices)...
Save : Spend : Total IncomeNext year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. Add another column for the ratio, representing next year's spending money
Save : Spend : Total Income : Next Year's Spend1 : ---------------- : ----------------------- : (1+r)
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? (1+r) is half of what? Well, (1+r) is half of (2+2r), so:
Save : Spend : Total Income : Next Year's Spend1 : (2+2r) : -------------------------- : (1+r)
And Total Income is the sum of the first two columns, so:
Save : Spend : Total Income : Next Year's Spend1 : (2+2r) : (3+2r) : (1+r)
In terms of r, what fraction of his income should Henry save this yearWell, looking at our ratio, that's 1/(3+2r)