gerad has a wooden board 11 feet long, he wants to cut it into 2 pieces so that the longer piece is 4 feet less than 4 times the length of the shorter piece, how long will each piece be

Shorter piece is 3 ft, longer piece is 8 ft

Step-by-step explanation:

Set up two equations ...

Let x be the length of the shorter piece, and let y be the length of the longer piece.

The whole board is 11 feet long, so

x + y = 11

He wants the longer piece to be 4 feet less than 4 times the length of the shorter board, so

y = 4x - 4

Substitute the second equation into the first equation ...

x + 4x - 4 = 11 (y becomes 4x - 4)

Now solve for x

5x = 15 (combine like terms, add 4 to both sides)

x = 3 (divide both sides by 5)

Now substitute 3 in for x in either equation and solve for y ...

y = 4 (3) - 4

y = 12 - 4

y = 8