Question

Xavier, Yessie, and Zorro each choose a different favorite positive fraction. Each fraction is in simplest form. Yessie's fraction is the reciprocal of Xavier's. Zorro multiplies his favorite fraction by Xavier's and finds a product of 12/35. Zorro then multiplies his favorite fraction by Yessie's fraction and finds a product of 15/7. What is each person's favorite fraction?

Answer 1

Let Xavier's favourite fraction be a/b, Yessie's favourite fraction = b/a and Zorro's favourite fraction = c/d,

c/d x a/b = 12/35 . . . . . . . . (1)
c/d x b/a = 15/7 . . . . . . . . (2)

(1) x (2) = c/d x a/b x c/d x b/a = 12/35 x 15/7
 c^2 / d^2 = 36/49
c^2 = 36
c = 6
d^2 = 49
d = 7

Xaviers favourite fraction = 12/35 / 6/7 = 2/5
Yessies favourite fraction = 5/2
Zorro favourite fraction = 6/7