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Simplifying algebraic expressions

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by pullagurla » Thu Sep 02, 2010 10:40 pm
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 has
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
d1/r+3
e)1/2r+3

Solve using picking numbers
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Source: — Problem Solving |

by Rahul@gurome » Fri Sep 03, 2010 3:19 am
pullagurla 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 has 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
d1/r+3
e)1/2r+3

Solve using picking numbers
Let Henry's income = $100 and his savings = $25. This means he spends $100 - $25 = $75
Fraction of the income that Henry should save this year = 25/100 = 1/4 (it is expressed in terms of r)
For each dollar he saved last year he should spend (r+1) next year.
By the given condition, 25(r+1) = 75/2 or r + 1 = 3/2 or r = 1/2
Put r=1/2 in the given choices and the one which gives 1/4 is the right answer.
1/2r + 3 = 1/2(1/2) + 3 = 1/4

The correct answer is [spoiler](E)[/spoiler].
Rahul Lakhani
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