A piece of wood is cut into three pieces in the ratio 2:3:5. If the longest piece is 15 in longer than the shortest piece, find the lengths of the piece of wood.

5/10x = 2/10x + 15

5/10x - 2/10x = 15

3/10x = 15

x = 15 * 10/3

x = 150/3

x = 50

2/10 (50) = 100/10 = 10 in ... shortest piece

3/10 (50) = 150/10 = 15 in ... middle piece

5/10 (50) = 250/10 = 25 in ... longest piece