The force F (in pounds) required to push a sofa across a floor varies directly as the weight w (in pounds) of the sofa.

Question

A person can push a 70 pound sofa across a wood floor by using a force of 30 pounds. Find an equation that describes the relationship between w and f

Answer 1

Force varies directly as weight can be written as

F=kw where k is the constant

When F=30 w=70

Substitute into equation

30=k70

Divide both sides by 70

30/70 = k

Reduce k=3/7

Put back in equation

F=(3/7)w