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A 26ft board is cut into three pieces at a sawmill. The second piece is 5ft longer than the first, and the third piece is 1ft longer than the second. What are the lengths of the three pieces?

User Jeff Warnica
by
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1 Answer

10 votes
10 votes

ANSWER

First piece = 5 ft

Second piece = 10 ft

Third piece = 11 ft

Explanation

What to find? The length of the three pieces of board

Given parameters

The total length of the board = 26ft

Let the length of the first piece = x ft

The length of the second piece is 5ft longer than the first

Mathematically.

Second piece = (x + 5) ft

The third piece of the length is 1 ft longer than the second piece

Recall that, second piece = (x + 5)

Hence, the third piece = 2nd piece + 1ft

Third piece = (x + 5) ft + 1 ft

WRITE THE LENGTH IN TERMS OF X

• First piece = x ft

,

• Second piece = (x + 5) ft

,

• Third piece = (x + 5) + 1

The next thing is to write an equation to find x

Total length = first piece + second piece + third piece


\begin{gathered} 26\text{ = x + (x + 5) + (x + 5) + 1} \\ \text{open the parentheses} \\ 26\text{ = x + x + 5 + x + 5 + 1} \\ \text{Collect the like terms} \\ 26\text{ = x + x + x + 5 + 5 + 1} \\ 26\text{ = 3x + 11} \\ Substract\text{ 11 from both sides} \\ 26\text{ - 11 = 3x + 11 - 11} \\ 15\text{ = 3x} \\ \text{Divide both sides by 3} \\ (15)/(3)\text{ = }(3x)/(3) \\ x\text{ = 5 ft} \end{gathered}

Find the length of each piece

First piece = 5ft

Second piece = (x + 5) ft

x = 5

second piece = 5 + 5

Second piece = 10ft

Third piece = (x + 5) + 1

Third piece = ( 5 + 5) + 1

Third piece = 10 + 1

Third piece = 11 ft

User Vishal Yadav
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