The strength of a rectangular beam varies jointly with its width and the square of its thickness. if a beam 7 7 inches wide and 3 3 inches thick supports 2520 2520 pounds, how much can a beam of the same material that is 2 2 inches wide and 1 1 inch inch thick support?

To solve the joint variation question we proceed as follows:

let the strength be p, the width be w, and thickness be t.

thus:

p=kwt

where k is the constant of proportionality.

p=2520 when w=7 and t=3

thus

2520=7*3*k

hence

k=120

thus the formula for variation is:

p=120wt

hence the value of p when w=2 in and t=1 in will be:

p=120*2*1

p=240 pounds