A 33-foot-long speaker wire is to be cut into three pieces. One piece is to be 11 feet long. Of the remaining pieces, one must be 2 feet less than 3 times the length of the other. Find the length of the shorter piece
Let x = shorter piece, then 3x-2 = other piece.
11 + x + (3x-2) = 33
Solve for x.
x=6
Let's call the length of the shorter piece "x".
We know that the total length of the speaker wire is 33 feet.
From the given information, we can determine the length of the other two pieces.
One piece is given to be 11 feet long, so the remaining length of the other two pieces will be:
33 feet - 11 feet = 22 feet.
Let's assume that the length of the longer piece is "y". According to the problem, it is 2 feet less than 3 times the length of the shorter piece.
So, we can express this relationship as:
y = 3x - 2
Now we can solve for the lengths of the remaining pieces.
We have two equations:
x + y = 22 (equation 1)
y = 3x - 2 (equation 2)
Substituting equation 2 into equation 1, we get:
x + 3x - 2 = 22
Combining like terms, we have:
4x - 2 = 22
Adding 2 to both sides, we get:
4x = 24
Dividing both sides by 4, we get:
x = 6
Therefore, the length of the shorter piece is 6 feet.
To find the length of the shorter piece, let's assume the length of the shorter piece as 'x'.
We are given that one piece is already 11 feet long. So, subtracting this from the total length, we have 33 - 11 = 22 feet of wire remaining.
Now, we are told that one of the remaining pieces must be 2 feet less than 3 times the length of the other piece. Let's call the length of the other piece 'y'. So, according to the given information, we have:
y = 3x - 2
Also, we know that the sum of the lengths of the two remaining pieces is equal to the remaining length of wire, which is 22 feet:
x + y = 22
Substituting the value of y from the first equation into the second equation, we get:
x + (3x - 2) = 22
Simplifying the equation, we have:
4x - 2 = 22
Adding 2 to both sides of the equation:
4x - 2 + 2 = 22 + 2
4x = 24
Dividing both sides by 4, we get:
x = 6
Therefore, the length of the shorter piece is 6 feet.