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.
Well, if we let the length of the shorter piece be x, then the longer piece would be 3x + 4 feet. Now, together they need to add up to the length of the original board, which is 12 feet. So, we can set up the equation x + (3x + 4) = 12.
Let me solve that for you:
4x + 4 = 12
4x = 8
x = 2
So, the shorter piece is 2 feet long, and the longer piece is 3(2) + 4 = 10 feet long.
But hey, at least now you'll have two pieces to work with if you ever need a makeshift ruler!
Let's let x represent the length of the shorter piece.
According to the problem, the longer piece is 4 feet longer than 3 times the shorter piece.
So, the length of the longer piece can be written as 3x + 4.
The sum of the lengths of the two pieces must be equal to the length of the original board, which is 12 feet.
Therefore, we can set up the equation:
x + (3x + 4) = 12
Now, let's solve for x:
4x + 4 = 12
Subtract 4 from both sides:
4x = 8
Divide by 4:
x = 2
So, the shorter piece is 2 feet long.
Now let's find the length of the longer piece:
3x + 4 = 3(2) + 4 = 6 + 4 = 10
The longer piece is 10 feet long.
Therefore, the lengths of the two pieces are 2 feet and 10 feet, respectively.
To solve this problem, we'll use the information given and set up an equation to represent the situation.
Let's assume that the shorter piece is x feet long. According to the problem, the longer piece is 4 feet longer than 3 times the shorter piece. Therefore, the length of the longer piece can be represented as (3x + 4).
The total length of the board is given as 12 feet. So, we can set up the equation:
x + (3x + 4) = 12
Now, let's solve the equation to find the value of x, which represents the length of the shorter piece:
4x + 4 = 12
Subtract 4 from both sides of the equation:
4x = 8
Divide both sides by 4:
x = 2
Now that we have found the length of the shorter piece, we can substitute this value back into our expression for the longer piece:
Length of longer piece = 3x + 4 = 3(2) + 4 = 10
Therefore, the lengths of the two pieces are 2 feet and 10 feet, respectively.