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

The length of what is left would be 1 1/2 feet long.