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A 45​-inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.

Respuesta :

The lengths of the three pieces are 5 Inches, 15 Inches and 25 Inches.

How to determine the lengths

From the information given, we have:

  • The length of the first piece = x
  • The second piece = 3x
  • The third piece = 5x
  • Total = 45 Inches

Now let's equate all the lengths to the total, we have:

x + 3x + 5x = 45

collect like terms

9x = 45

Make 'x' the subject of formula

9x = 45

x = 45/ 9

x = 5

To find the lengths:

First piece = x = 5 Inches

Second piece = 3x = 3 (5) = 15 Inches
Third piece = 5x = 5 ( 5) = 25 Inches

Thus, the lengths of the three pieces are 5 Inches, 15 Inches and 25 Inches.

Learn more about algebraic expressions here:

https://brainly.com/question/723406

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