A 100-foot rope is cut into three pieces. The first piece is three times as long as the second, and the third piece is 30 feet shorter than the second. How many feet long is the shortest piece?
Set the length of the second peice to be \(x\), then the first piece would have a length of \(3x\), and the third piece would have a length of \(x-30\). Then we obtain the equation \(x+3x+x-30=100\) , or \(5x-30=100\). Solving, we get that x = 26, but this makes the third piece have negative length, so this is impossible.