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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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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Total = n

savings = n - 4n/5

= n/5 per week.

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

= 2500 /n.

The best answer is B.

This can be thought of as a conversion problem. We are converting $500 to weeks.

$500 • \(\frac{1 week}{n/5 dollars}\)

\(\frac{2500}{n weeks}\)