A 37-in. board is cut into three pieces. The second piece is 3in longer than the first piece. The third piece is 4 in. longer than the second piece. how long is each piece?
a 37-in. board
Let x be the length of the shortest board. The second piece is 3 inches longer than the first, or (x+3). The third piece is 4 inches longer than the second, or (x+3+4) which is (x+7). The original board was 37 inches, so the three pieces have to add up to 37:
(x) + (x+3) + (x+7) = 37
Combine terms: 3x + 10 = 37
Subtract 10 from each side: 3x + 10 - 10 = 37 - 10
So: 3x = 27
Divide both sides by 3: 3x/3 = 27/3
So x = 9.
The shortest board was x, so it's 9 inches. The second board was x+3, or 12 inches. The third board was x+7, or 16 inches. Add them together and you get the original 37 inches.