Respuesta :
ANSWER
First piece = 5 ft
Second piece = 10 ft
Third piece = 11 ft
STEP-BY-STEP 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
[tex]\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} \\ \frac{15}{3}\text{ = }\frac{3x}{3} \\ x\text{ = 5 ft} \end{gathered}[/tex]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
