A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces
12ft-x=3x+4
12ft- x-3x=4ft
12ft-4x =4ft
-4x=-8ft
x=2ft
correct
To solve this problem, you can follow these steps:
Step 1: Let's assume the shorter piece is x feet long.
Step 2: According to the problem, the longer piece is 4 feet longer than 3 times the shorter piece. So, the length of the longer piece is 3x + 4 feet.
Step 3: Now, we are given that the total length of the board is 12 feet. So, we can set up the equation: length of shorter piece + length of longer piece = total length of the board.
Step 4: Substituting the values from Step 1 and Step 2 into the equation, we get: x + (3x + 4) = 12.
Step 5: Simplifying the equation, we have: 4x + 4 = 12.
Step 6: Subtracting 4 from both sides of the equation, we get: 4x = 8.
Step 7: Dividing both sides of the equation by 4, we get: x = 2.
Step 8: Therefore, the shorter piece is 2 feet long.
Step 9: Substituting x = 2 into the expression for the longer piece (3x + 4), we get: 3(2) + 4 = 6 + 4 = 10.
Step 10: Therefore, the longer piece is 10 feet long.
Therefore, the lengths of the two pieces are 2 feet and 10 feet, respectively.