A 74-foot length of wire is to be cut into 2 pieces, so that the longer piece is four feet longer than six times the shorter piece. Find the length of each piece.
x = shorter piece
x + 6x + 4 = 74
7x = 70
x = 10
Sue is right but the answer is incomplete. The second or longer piece should be:
6(10) + 4
60 +4 = 64 foot
Let's assume that the shorter piece of wire has a length of x feet.
According to the given information, the longer piece is four feet longer than six times the shorter piece. So, the length of the longer piece is (6x + 4) feet.
Now, we know that the total length of the wire is 74 feet. Therefore, we can write the equation:
x + (6x + 4) = 74
Simplifying the equation:
7x + 4 = 74
Subtracting 4 from both sides:
7x = 70
Dividing both sides by 7:
x = 10
So, the shorter piece of wire is 10 feet long.
Plugging this value back into the equation for the longer piece:
6x + 4 = 6(10) + 4 = 64
Therefore, the longer piece of wire is 64 feet long.
In summary, the length of each piece of wire is 10 feet and 64 feet, respectively.
To solve this problem, we can set up a system of equations. Let's denote the length of the shorter piece as "x" and the length of the longer piece as "y."
We are given two pieces of information in the problem statement:
1. The sum of the lengths of the two pieces is 74 feet, which can be expressed as: x + y = 74.
2. The longer piece is four feet longer than six times the shorter piece, which can be expressed as: y = 6x + 4.
Now, we can solve this system of equations using either substitution or elimination methods.
Let's solve it using the substitution method:
1. Substitute the expression for y from the second equation into the first equation: x + (6x + 4) = 74.
2. Simplify the equation: 7x + 4 = 74.
3. Subtract 4 from both sides: 7x = 70.
4. Divide both sides by 7: x = 10.
Now that we have found the value of x, we can substitute it back into one of the equations to solve for y:
Using the second equation: y = 6x + 4,
Substituting x = 10: y = 6(10) + 4,
Simplifying the equation: y = 60 + 4,
y = 64.
Therefore, the length of the shorter piece is 10 feet, and the length of the longer piece is 64 feet.