A cable 40 feet long is cut into three pieces so the length of the second piece is 4 times the length of the first piece, and the third piece is five more than twice as long as the first piece. Find the length of the pieces.
Let x = first piece, then the second piece = 4x and the third = 2x + 5.
These three terms should add to 40.
I'll let you do the calculations.
let x=x+x+x=40 then
To solve this problem, let's assume the length of the first piece is x feet.
According to the given information:
The second piece is 4 times the length of the first piece, so its length is 4x feet.
The third piece is five more than twice the length of the first piece, so its length is 2x + 5 feet.
Now, we can set up an equation to represent the total length of the cable:
x + 4x + (2x + 5) = 40
Simplifying the equation:
7x + 5 = 40
7x = 35
x = 5
Now that we have found the value of x, we can substitute it back into the expressions for the second and third pieces' lengths:
Second piece: 4x = 4 * 5 = 20 feet
Third piece: 2x + 5 = 2 * 5 + 5 = 15 feet
So, the length of the three pieces is:
First piece: 5 feet
Second piece: 20 feet
Third piece: 15 feet