Having Problems with these OG Questions...

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Having Problems with these OG Questions...

by okigbo » Wed Sep 09, 2009 11:22 am
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 yr, the amount he has available to spend will be equal to half the amount he spends this year?

a. 1/r+2
b. 1/2r+2
c. 1/3r+2
d. 1/r+3
e. 1/2r+3

OA: [spoiler]E[/spoiler]


John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours and Mary worked for 2 hours less than John. If Mary gave John y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y that John was paid in advace?

a. 4y
b. 5y
c. 6y
d. 8y
e. 9y

OA: [spoiler]E[/spoiler]
[/spoiler]
Source: — Problem Solving |

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Answer to problem 1

by rafodr » Wed Sep 09, 2009 1:47 pm
Lets call
I = Income
SV = Amount saved this year
SP = Amount spent this year

The question, in other words, is: "Find SV/I in order to SV*(1+r)=1/2*SP"

1. You know that I = SV + SP
2. From (1) -> SP = I - SV
3. Plug (2) into the eq. SV*(1+r)=1/2*SP, and find SV
4. You'll find that SV = I/(3+2*r)
5. Plug SV = I/(3+2*r) into SV/I
6. SV/I = 1/(3+2*r), that's your answer

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For your second problem

by rafodr » Wed Sep 09, 2009 1:52 pm
You have to equalize the hourly wages of John and Mary after Mary gives John the y dollars, so:

John Mary
(x + y)/10 = (x - y)/(10 - 2)

The amount that John is paid in advance is x, so find x in terms of y

8x + 8y = 10x - 10y
x = 9y