When the store had sold 2/9 of the boots that were on display, they brought out another 34 pairs from the stock room. if that gave them 174 pairs of boots out, how many pairs were on display originally? show work

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.