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Jacob’s weekly take-home pay is n dollars. Each week he uses

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Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 15 Jul 2018, 07:35
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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 \(625n\)

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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 15 Jul 2018, 08:35
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Bunuel 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 ?


Jacob’s weekly take-home pay = n $
Jacob’s weekly expenses = 4n/5 $
Amount saved each week = n - (4n/5) = n/5 $

Thus,
Number of weeks required to save $500 @ n/5 $ per week = 500 / (n/5) = 2500 / n

Hence, B.
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Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 15 Jul 2018, 10:34
Bunuel 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 \(625n\)



Savings in each week = n - 4n/5

= n/5

Week needed to save $500 = $500/ (n/5)

= 2500 / n

Thus the best answer is B.
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 15 Jul 2018, 17:26
Bunuel 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 \(625n\)



So two ways..
1) algebraic as shown above too..
Savings in a week -> 1-4n/5=n/5
So savings n/5 in 1 week
Savings 1 in 5/n weeks
Savings 500 in 500*5/n=2500/n weeks

2) substitution
Take a smart number, say n = 100..
Savings =100/5=20, thus number of weeks =500/20=25
Check the choices..
B. 2500/n =2500/100=25.....yes

B
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 16 Jul 2018, 07:51
Bunuel 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 \(625n\)


Jacob's weekly savings = \(n - \frac{4n}{5}\)

Or, Jacob's weekly savings = \(\frac{n}{5}\)

Time required to save $ 500 is \(\frac{500*5}{n}\) = \(\frac{2,500}{n}\), Answer must be (B)
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses  [#permalink]

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New post 19 Jul 2018, 11:40
Bunuel 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. Each week he uses &nbs [#permalink] 19 Jul 2018, 11:40
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