<PRE><B>Question 243079</B>
The product of two numbers is 128 and their quotient is 8. What are the numbers?


Let the 1st number be F, and the 2nd S


Since their product is 128, we can say that FS = 128 -------- (i)


Also, since their quotient is 8, then we can say that {{{F/S = 8}}}------ (ii)


Solving for F in eq (ii), we get: F = 8S


Substituting 8S for F in eq (i), we get: 8S(S) = 128


{{{8S^2 = 128}}}-------- {{{8S^2 - 128 = 0}}}


{{{8(S^2 - 16) = 8(0)}}}-------- Factoring out GCF, 8


{{{S^2 - 16 = 0}}}-------- (S - 4)(S + 4) = 0


Therefore, S, or the 2nd number is 4, or - 4


If the 2nd number is 4, then the 1st number is F(4) = 128, which makes F = 32


If the 2nd number is -4, then the 1st number is F(-4) = 128, which makes F = -32


Therefore, the numbers are either {{{highlight_green(4_and_32)}}}, or {{{highlight_green(-4_and_-32)}}}. </PRE>