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

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