Question 374113
"The product of two numbers is 10 less than 16 times the smaller" ___ S * L = 16S - 10


"twice  the smaller is 5 more than the larger" ___ 2S = L + 5 ___ 2S - 5 = L


substituting ___ S(2S - 5) = 16S - 10 ___ 2S^2 - 21S + 10 = 0


2S^2 - 21S = -10 ___ S^2 - (21/2)S = -5


S^2 - (21/2)S + (-21/4)^2 = -5 + (-21/4)^2


(S - (21/4)^2 = (-80/16) + (441/16) = 361/16 = (±19/4)^2


S = (19/4) + (21/4) = 10 ___ or ___ S = (-19/4) + (21/4) = 1/2


substituting ___ 2(10) - 5 = L ___ L = 15 ___ or ___ L = 2(1/2) - 5 = -4



using the negative root causes the "larger" to be the "smaller" , and vice versa