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Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5

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Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5  [#permalink]

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New post 14 Oct 2018, 23:36
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (01:18) correct 16% (02:10) wrong based on 50 sessions

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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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Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5  [#permalink]

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New post 15 Oct 2018, 00:18
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 \(625n\)


Take Home weekly pay = n

Weekly Saving = n - (4/5)n = n/5

Weeks to be spent to save $500 = 500/(n/5) = 2500/n

Answer: Option B
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5  [#permalink]

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New post 15 Oct 2018, 03:57
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 \(625n\)


One approach

Remaining = n - \(\frac{4n}{5}\) = \(\frac{1n}{5}\)

500/(1n/5) =\(\frac{2500}{n}\)

Another approach would be to pick numbers n = 10

\(\frac{4n}{5} = 8\)

remaining 2

\(\frac{500}{2} = 250\)

\(\frac{500}{10} = 50\) incorrect

\(\frac{2500}{10} = 250\) correct.

Answer choice B
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5  [#permalink]

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New post 15 Oct 2018, 07:46
Let n be 100
4n/5 = 80 (expenses) & remaining 20 (savings)

500/20 = 25 days

(B) 2500/100 = 25

Answer is B
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5  [#permalink]

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New post 15 Oct 2018, 20:07
In this question,i used this approach

Took salary earned by Jacob per week as 50 dollars

In this his expenses were 40 dollars and he saved 10 dollars

It is given that he saved 500 dollars after some weeks.

If you can notice as you increase the number of weeks, an AP is formed in the amount which he is saving per week,To Explain this

1st week $50 Expenses $40 Saved $10
2st week $100 Expenses $80 Saved $20
3st week $150 Expenses $120 Saved $30

so in the
50th week
he saved 500 dollars, calculated by, last term = a + (n-1) d
where a =10, d =10 and last term = 500

Now you have to find out of the answer options which option will give you 50 as the answer

Making the answer as

I feel Once you realize its an AP this is an easy approach.
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Re: Jacob’s weekly take-home pay is n dollars. Each week he uses 4n/5   [#permalink] 15 Oct 2018, 20:07
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