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mehravikas
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IMO E
OA? if i were right, i will post my explanations.
Amount saved in terms of r
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jeffxujian
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jeffxujian
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never mind, i saw the answer. Following is the method i used:
Assume this guy makes 100 this year, save 25 and spend 75. so the saving consists 25% of his total income of this year.
We are also given that for every 1 dollar saved this year, 1+r will be available to spend next year, so 25 saved this year will become 25*<1+r>, and also we want this amount to equal to half of the amount we spent this year, so the equation will be as follows:
25*<1+r> = 75/2<37.5>
r=.5
now we test each answer choice using r= .5 and we want an answer choice that gives us 25% as a result. E does.
Assume this guy makes 100 this year, save 25 and spend 75. so the saving consists 25% of his total income of this year.
We are also given that for every 1 dollar saved this year, 1+r will be available to spend next year, so 25 saved this year will become 25*<1+r>, and also we want this amount to equal to half of the amount we spent this year, so the equation will be as follows:
25*<1+r> = 75/2<37.5>
r=.5
now we test each answer choice using r= .5 and we want an answer choice that gives us 25% as a result. E does.
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mehravikas
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Thanks. I followed the same steps but was confused how to get the answer after plugging in the value of r.
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jeffxujian
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remember we are trying to plug in r=.5 to get a value equals .25, so
a. 1/.5+2=.4
b. 1/1+2 =.33
c. 1/3.5
d. 1/3.5
e.1/1+3 = .25 correct answer
a. 1/.5+2=.4
b. 1/1+2 =.33
c. 1/3.5
d. 1/3.5
e.1/1+3 = .25 correct answer
An answer without substitution
Total = T
saved T/x
so spent
= T - T/x
equation
(1+r) T / x = (T - T/x) * 1/2
(1+r)/x = 1/2 - 1/2x
(3+2r) / 2x = 1/2
1/x = 1/(3+2r)
Ans E
we need fraction so fraction is 1/x and not x
Total = T
saved T/x
so spent
= T - T/x
equation
(1+r) T / x = (T - T/x) * 1/2
(1+r)/x = 1/2 - 1/2x
(3+2r) / 2x = 1/2
1/x = 1/(3+2r)
Ans E
we need fraction so fraction is 1/x and not x
