max A=lw subject to l+3w=227

l= 227-3w

maximize w(227-3w) = 227w - 3w^2

Since the title is algebra, I will solve by completing the square.

-3(w^2 - 227w/3 + (227/6)^2) + 3(227/6)^2 =

-3(w - 227/6)^2 + 3(227/6)^2

If w = 227/6, l = 227 - 3(227/6)) = 227/2

A = 227^2/12

Answer: l = 227/2; w = 227/6; A = 227^2/12

(If this were calculus, we would take the derivative of 227w - 3w^2 and set equal to 0, and prove it was a maximum by taking the second derivative and noticing that it was negative everywhere).