Let us assume number of boots pairs were on display originally = x.
We are given 2/9 of the total boots pairs we sold.
So, 2/9 of x boots pairs were sold, that is
Number of boots pairs were sold = 2/3 x.
Number of boots pairs brought out from store = 34.
Remaining pairs of boots = 174 pairs.
So, we can setup an equation,
Total number of boots pairs - First number of boots pairs sold + number of boots pairs brought out from store = Remaining pairs.
x - 2/9 x +34 = 174.
Subtracting 34 on both sides, we get
x - 2/9 x = 34-34 = 174-34
x- 2/9 x = 140 .
Simplifying left fracions by taking common denominator,
9/9 x- 2/9 x = 140
(9x-2x)/9 = 140.
7/9 x = 140.
Multiplying both sides by 9.
9* 7/9 x = 9*140.
7x = 1260.
Dividing both sides by 7.
7x/7 = 1260/7
x= 180.
Therefore, 180 pairs were on displayed originally.
