The distance a spring stretches varies directly as the force applied. if a force of 140 newtons stretches a spring 4 cm, how much will a force of 350 newtons stretch the same string?

Let x represent the distance of spring stretch and F be the force. Then k is the constant of proportionality and we have, by direct proportions:
                                     F = kx
When F = 140, x = 4, thus k = F/x = (140 Newtons)/(4 cm) = 35 Newtons/cm.
Then, since x = F/35
                                      x = 350/35
                                      x = 10cm
The answer to this question is 10 cm.

Wow. that is a really cool question.