a 9 foot board is cut into two pieces .one is 3.5 feet longer than the other. how long is the longer piece?
x + x + 3.5 = 9
2x = 5.5
x = 2.75
The shorter piece is 2.75 feet long.
To find the length of the longer piece, let's call the length of the shorter piece x. According to the information given, the longer piece is 3.5 feet longer than the shorter piece.
So, the length of the longer piece would be x + 3.5.
Since the total length of the board is 9 feet, we can write an equation:
x + (x + 3.5) = 9
To solve this equation, we can simplify and combine like terms:
2x + 3.5 = 9
Next, we can isolate the variable by subtracting 3.5 from both sides:
2x = 9 - 3.5
2x = 5.5
Finally, divide both sides by 2 to solve for x:
x = 5.5 / 2
x = 2.75
So, the length of the shorter piece is 2.75 feet.
To find the length of the longer piece, we can substitute this value into the equation:
Length of longer piece = x + 3.5 = 2.75 + 3.5 = 6.25 feet.
Therefore, the longer piece is 6.25 feet long.