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Jacob’s weekly take-home pay is n dollars

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Jacob’s weekly take-home pay is n dollars [#permalink] New post 23 Jan 2016, 05:29
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Jacob’s weekly take-home pay is n dollars. Each week he uses \(\frac{4n}{5}\) dollars for expenses and saves the rest. At those rates, how many weeks will it take Jacob to save $500, in terms of n ?

A \(\frac{500}{n}\)

B \(\frac{2,500}{n}\)

C \(\frac{n}{625}\)

D \(\frac{n}{2,500}\)

E \(625n\)


Practice Questions
Question: 16
Page: 461
Difficulty: medium
[Reveal] Spoiler: OA

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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 23 Jan 2016, 06:03
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Solution

Jacob’s weekly expenses are \(\frac{4n}{5}\) dollars. Therefore, the amount he saves each week is equal to his weekly take-home pay minus his weekly expenses, are

\(n\) - \(\frac{4n}{5}\) = \(\frac{n}{5}\) Dollars.

So number of weeks required by Jocob to save $500 at the rate of $\(\frac{n}{5}\) per week = 500/ \(\frac{n}{5}\) = \(\frac{2500}{n}\).

Hence Option B is the correct solution.
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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 14 Jul 2016, 14:24
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sandy wrote:
Jacob’s weekly take-home pay is n dollars. Each week he uses \(\frac{4n}{5}\) dollars for expenses and saves the rest. At those rates, how many weeks will it take Jacob to save $500, in terms of n ?

A \(\frac{500}{n}\)
B \(\frac{2,500}{n}\)
C \(\frac{n}{625}\)
D \(\frac{n}{2,500}\)
E \(625n\)



We can also use the INPUT-OUTPUT approach.
Let's say n = 5 (Jacob takes $5 home each week)
This means Jacob SPENDS $4 each week.
So, he SAVES $1 each week

At this rate, how many weeks are needed to save $500?
It will take 500 weeks.

So, when we INPUT n = 5, the OUTPUT (the answer to the question) is 500

Now check the answer choices to see which one yields an OUTPUT of 500 when we INPUT n = 5

A) 500/5 = 100 ELIMINATE
B) 2500/5 = 500 KEEP
C) 5/625 = less than 1 ELIMINATE
D) 5/2500 = less than 1 ELIMINATE
E) 625(5) = over 3000 ELIMINATE

Answer: B
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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 19 Jul 2018, 11:40
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sandy wrote:
Jacob’s weekly take-home pay is n dollars. Each week he uses \(\frac{4n}{5}\) dollars for expenses and saves the rest. At those rates, how many weeks will it take Jacob to save $500, in terms of n ?

A \(\frac{500}{n}\)

B \(\frac{2,500}{n}\)

C \(\frac{n}{625}\)

D \(\frac{n}{2,500}\)

E \(625n\)


We see that 1 - (4n/5) = n/5 is saved each week. Let’s let w = the number of weeks it will take to save 500 dollars and create the equation:

n/5 x w = 500

nw = 2500

w = 2500/n weeks.

Answer: B
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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 19 Jul 2018, 12:24
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sandy wrote:
Jacob’s weekly take-home pay is n dollars. Each week he uses \(\frac{4n}{5}\) dollars for expenses and saves the rest. At those rates, how many weeks will it take Jacob to save $500, in terms of n ?

A \(\frac{500}{n}\)

B \(\frac{2,500}{n}\)

C \(\frac{n}{625}\)

D \(\frac{n}{2,500}\)

E \(625n\)


Practice Questions



Question: 16
Page: 461
Difficulty: medium



Total = n

savings = n - 4n/5

= n/5 per week.

So, 500 / (n/5) = 500 * 5/n

= 2500 /n.

The best answer is B.
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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 04 Oct 2018, 01:13
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what he saves from his salary

(4n/5)-1 = (1n/5)

dvide what amount required to save(500$) with saving ratio (1n/5) in order to dertmine weeks required to save

500 /(1n/5) = 500*(1/n/5) =2500/n

Answer is (B)
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Re: Jacob’s weekly take-home pay is n dollars [#permalink] New post 22 Aug 2019, 09:45
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This can be thought of as a conversion problem. We are converting $500 to weeks.

$500 • \(\frac{1 week}{n/5 dollars}\)

\(\frac{2500}{n weeks}\)
Re: Jacob’s weekly take-home pay is n dollars   [#permalink] 22 Aug 2019, 09:45
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