97/19=w+{1/[x+(1/y)]}

[dagr8est]

If 97/19=w+{1/[x+(1/y)]}, where w, x, y are all positive integers, then w+x+y equals:
A) 16
B) 17
C) 18
D) 19
E) 26

I solved this problem in a "non-standard" way and got the answer of 16. Can anyone confirm that answer and show how you would solve this question "properly"?

Here's how I got w+x+y=16. Again, I stress that this is a "non-standard" solution. :lol:

97/19=w+{1/[x+(1/y)]}
5+(2/19)=w+{1/[x+(1/y)]}

By inspection, w=5 and:
1/[x+(1/y)]=2/19
19=2[x+(1/y)]
9.5=x+(1/y)

By inspection, x=9 and y=2.

w+x+y=5+9+2=16

 

[Gene]

You started out perfectly but you could have kept up that method. You recognized that the fractional parts had to be equal.
2/19 = 1/[x+(1/y)]
19/2 = x+(1/y)
9 + 1/2 = x+(1/y)
x = 9

1/2 = 1/y
2 = y

Same answer but it seems neater to follow the same logic.
---------------------
Gene