A carpenter wants to cut an 18-foot board into two pieces so that one piece is 3 feet shorter than twice the shorter piece. Where should he make the cut?
---?--- ft from one end
L = length of board piece
a = length of first piece
b = length of second ( shorter ) piece
a = 2 b - 3
L = 18 = a + b = 2 b - 3 + b = 3 b - 3
3 b - 3 = 18 Add 3 to both sides
3 b - 3 + 3 = 18 + 3
3 b = 21 Divide both sides by 3
3 b / 3 = 21 / 3
b = 7 ft
a = 2 b - 3
a = 2 * 7 - 3 = 14 - 3 = 11 ft
a carpenter cut a 3- meter board into four pieces of equal length . how
many centimeters long was each piece?
i need help with my homework
To solve this problem, we need to set up an equation based on the given information and solve for the position of the cut.
Let's assume the length of the shorter piece is x feet.
According to the problem, the longer piece should be 3 feet shorter than twice the shorter piece. So, the length of the longer piece would be (2x - 3) feet.
Since the total length of the board is 18 feet, the sum of the lengths of the shorter and longer pieces should be equal to 18 feet. We can write this as an equation:
x + (2x - 3) = 18
Now, let's solve this equation to find the value of x, which represents the length of the shorter piece:
3x - 3 = 18
3x = 21
x = 7
Therefore, the shorter piece has a length of 7 feet.
To determine where the carpenter should make the cut, we need to find the distance from one end. Since the shorter piece is 7 feet long, we subtract 7 feet from the total length of the board:
18 - 7 = 11
The carpenter should make the cut 11 feet from one end of the board.
Thus, the answer is: ---11--- ft from one end.