## Algebra: A Combined Approach (4th Edition)

The shorter piece is $2$ ft long The longer piece is $8$ ft long
Step 1: The total length of the board is $10$ ft.. Step 2: We assume that the length of the shorter piece is $x$ ft.. Step 3: The length of the longer piece is therefore $4x$ ft.. Step 4: Since the shorter and longer piece together equal the total length of the board, $x+4x=10$. Step 5: Simplifying, $5x=10$ Step 6: $x=2$ ft Step 7: Therefore, the shorter piece is $2$ ft long while the longer piece is $2\times4=8$ ft long.