A24 inch board is cut into 3 pieces so that the second piece is twice as long as the first and the third is 3 times as long as the first puece. if x represents the length of the first piece find the lengths of all three pieces

The answer to your question is:  first piece = 4 in, second piece = 8 in, third piece = 12 in

Step-by-step explanation:

Data

total length = 24 inches

first piece = x in

second piece = 2x

third piece = 3x

Equation

               x + 2x + 3x = 24

               6x = 24

               x = 24/6

               x = 4               length of the first piece

second piece = 2(4) = 8 inches

third piece = 3(4) = 12 inches

Step-by-step explanation:

The total length of the three pieces is ...

  x + 2x + 3x = 24 . . . . inches

  6x = 24 . . . . . . . . . . . collect terms

  x = 4 . . . . . the length in inches of the first piece

  2x = 8 . . . . the length in inches of the second piece

  3x = 12 . . . . the length in inches of the third piece

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