Word Problems, Working Backwards

Question

A store sold their entire inventory of Tvs in one month. The first week they sold 1/2 of their inventory. The second week they sold 1/3 of the remaining TVs. The third week they sold 3/4 od what was left. The fourth week they sold the remaining 8 TVs. How many TVs did the store sell in the entire month

Answer 1

working backwards...

week 3 they sold 3/4 of what was left and had 8 remaining in week 4

8 is 1/4 of what they had week 3

4*8=32 is what they had week 3

week 2 they sold 1/3 of what was left and had 32 left in stock

32 is 2/3 of what they had week 2 in stock

2/3 of what is 32 ?

(3/2)*32=48 in stock week 2

48 represents 1/2 the inventory because they sold 1/2 of the inventory in week 1

2*48=96 TVs were sold that month

Answer 2

Emily,

 

Let us assume that the store sold n TV's in the month

 

In first week they sold n/2 TV's

In second week they sold 1/3 of remaining n/2 i.e. n/6 TV's

TV's remaining after week 2 = n -n/2-n/6 = n/3

In third week they sold 3/4 of n/3 i.e. n/4 TV's

TV's remaining after week 3 = n/3 -n/4 = n/12

In 4th week they sold all of remaining TV's which is n/12 = 8

n = 96

 

Hence they sold 96 TV's in the month.