a 25 foot wire is to be cut so that the longer piece is one foot longer than 5 times the shorter.
find the length of each piece
thank you!
x + 5x+1 = 25
X+5x+1=25 x+5x=6x 6x+1=25 Now flip
25-1÷6= 25-1=24 24÷6=4 4=short piece
Now times by five and add 1 for longer piece.
4×5=20. 20+1=21 21=long
To find the lengths of the wire pieces, let's define the shorter piece as "x" and the longer piece as "y".
According to the problem, the longer piece is one foot longer than 5 times the shorter piece. So, we can write the equation:
y = 5x + 1
Now, we are also given that the total length of the wire is 25 feet. Thus, the sum of the two pieces should be equal to 25:
x + y = 25
Now we have a system of two equations:
1. y = 5x + 1
2. x + y = 25
To solve this system, we can use substitution or elimination method. Let's use substitution:
From equation 1, we can substitute the value of "y" in equation 2:
x + (5x + 1) = 25
Simplifying the equation:
6x + 1 = 25
Subtracting 1 from both sides:
6x = 24
Dividing both sides by 6:
x = 4
Now, we can substitute the value of "x" back into equation 1 to find the value of "y":
y = 5(4) + 1
y = 20 + 1
y = 21
Therefore, the shorter piece is 4 feet long and the longer piece is 21 feet long.