Cutting Steel

A 25 inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is one inch more than five times the length of the first piece. Find the lengths of the pieces.

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x = length of first piece
2x = length of second piece   {the second piece is twice as long as the first piece}
5x + 1 = length of third piece  {the third piece is one inch more than five times the length of the first piece}

The entire length of the piece of steel is 25 inches.

x + 2x + 5x + 1 = 25   {added the three pieces together and set equal to 25}
8x + 1 = 25   {combined like terms}
8x = 24   {subtracted 1 from each side}
x = 3   {divided each side by 8}
2x = 6   {substituted 3, in for x, into 2x}
5x + 1 = 16   {substituted 3, in for x, into 5x + 1}

first piece = 3 inches
second piece = 6 inches
third piece = 16 inches

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