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?

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

270 books in each shelves

29933333.33

step-by-step explanation:

6×10=604000000÷60=66666.6666766666.6667×449=29933333.33