on the morning of the sale, the store donated 50 pairs of shoes to a homeless shelter. then they sold 64% of their remaining inventory during the sale. how many pairs of shoes did they have at the start?
Let x be the total number of pairs of shoes at the start.
After donating 50 pairs to the homeless shelter, the store had x - 50 pairs of shoes left.
During the sale, they sold 64% of their remaining inventory, which means they sold 0.64(x - 50) pairs of shoes.
This means that they had (x - 50) - 0.64(x - 50) = 0.36(x - 50) pairs of shoes left after the sale.
Since they sold 64% of their remaining inventory during the sale, they must have had 100% - 64% = 36% of their inventory left after the sale.
So we have 0.36(x - 50) = 0.36x - 18 pairs of shoes left after the sale.
This means that 0.36x - 18 = x - 50.
Solving for x, we get:
0.36x - 18 = x - 50
0.64x = 32
x = 50
Therefore, the store had 50 pairs of shoes at the start.