Question

Math Contest problem, Solve please.

Answer 1

If m, n and p are positive integers with:

\[m+\frac{ 1 }{ n+\frac{ 1 }{ p } }=\frac{ 17 }{ 3 }\]

The value of n is:

A) 3 B) 4 C) 1 D) 17 E) 13

Answer 2

c.. n=1
since 17/3 = 5 + 2/3, i let m=5. so that leaves \(\large \frac{1}{n+\frac{1}{p}}=\frac{2}{3} \)
or
\(\large \frac{1}{\frac{np}{p}+\frac{1}{p}}=\frac{2}{3} \)
or
\(\large \frac{p}{np+1}=\frac{2}{3} \)

so if p=2, then np+1=3. so n=1