Final answer:
To solve for the length of the first piece of the board, we created an equation representing the total length of the board. After simplifying and solving, we determined that the first piece is 5 feet long.
Step-by-step explanation:
The student's question is about determining the lengths of two pieces of a board after it has been cut according to the given conditions. To solve the problem, we need to set up an equation based on the information provided:
Let the length of the first piece be x feet. Then, the second piece is 5 feet longer than twice the length of the first piece, which can be expressed as 2x + 5 feet. Since the total length of the board is 20 feet, we can set up the following equation:
x + (2x + 5) = 20
Combining like terms gives us:
3x + 5 = 20
Next, subtract 5 from both sides of the equation:
3x = 15
Last, divide both sides by 3 to find the value of x:
x = 5
Therefore, the length of the first piece is 5 feet.