Question

A reatil outlet is having a clearance sale on all the shoes in its inventory over a period of four days. On the first day it sells 1/4 of its inventory, on the second day it sells 1/2 of the remaining inventory , and on the third day it sells 1/6 of the remainder. What fraction of the original inventory is left of the sale?

PLease help me!!! i got 1/12 is that right and please explain if it is becuase i dont even know how i got it..

Answer 1

inventory ---- x
after day 1, inventory left = 3x/4
after day 2, inventory left = 3x/8
after day 3, inventory left = (5/6)(3x/8) = 5x/16

fraction of original is 5/16

check: suppose we had 240 items in the inventory
day 1, sold (1/4) of 240 , leaving 180
day 2, sold 1/2 of 180, leaving 90
day 3, sold 1/6 of 90, leaving 75
fraction is 75/240 = 5/16