Aperson can push a 160 -pound sofa across a carpeted floor by pushing with a force of 100 pounds. find an equation that describes the relationship between w and f.

Missing part in the heading of the question:
"The force f (in pounds) required to push a sofa across the floor varies directly as the weight w (in pounds) of the sofa"

F = 0.625 w

Explanation:
We are given that F in pounds varies directly with the weight of the sofa in pounds.
This means that:
F = kw
where:
F is the force
k is the constant of proportionality
w is the weight of the sofa

We are given that:
F is 100 pounds when w is 160 pounds

Substitute with these givens in the above equation to get the constant of proportionality k as follows:
F = kw
100 = 160k
k = 100 / 160
k = 0.625

This means that the equation describing the relation between the force and the weight of the sofa is:
F = 0.625 w

Hope this helps :)