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..
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
To determine the fraction of the original inventory that is left after the sale, we can follow the steps as explained:
First, let's assume that the original inventory of shoes is represented by the number 1 (for simplicity).
On the first day, the retail outlet sells 1/4 of its inventory. This means that only 3/4 of the original inventory remains (1 - 1/4 = 3/4).
On the second day, the outlet sells 1/2 of the remaining inventory. Hence, only 1/2 of the 3/4 that was left after the first day's sales is left (3/4 * 1/2 = 3/8).
On the third day, the outlet sells 1/6 of the remaining inventory. Therefore, only 5/6 of the 3/8 that was left after the second day's sales is left (3/8 * 5/6 = 15/48 = 5/16).
So, after the three days of sales, 5/16 of the original inventory is left.
Therefore, the fraction of the original inventory that remains after the sale is 5/16.
Your answer of 1/12 is not correct. To clarify how you obtained it, please provide your calculations or reasoning.