algebra beam problems

Question

The strength of a rectangular beam varies jointly as its width and the square of its depth. If the strength of a beam 4 inches wide by 12 inches deep is 1800 pounds per square inch, what is the strength of a beam 5 inches wide and 12 inches deep?

Answer 1

s = kwd^2 = 1800 = k(4)(12^2

k = 1800/144(4) = 450/12(12) = 225/72 25/8

s = 25wd^2/8

s = 25(5)(144)/8= 125(36/2) = 125(18) = 2250 lbs/in^2

or

= 5/4 x 1800 = 5(450 = 2250 lbs/in^2