+42 Amy and Ben each picked a positive whole number. The sum of Amy’s
and Ben’s numbers was 23. The product of Amy’s and Ben’s numbers
was 126. If Amy’s number was greater than Ben’s number, what is the
value of Amy’s number minus Ben’s number?
+129850 Well....we don't anyone dying on here....so...here's a life preserver....
Let Amy's number = x and Ben's = y
And we know that
x + y = 23 (1)
Also
xy =126 ⇒ y =126/x (2)
Sub (2) into (1) for y and we have that
x + 126/x = 23 multiply through by x
x^2 + 126 = 23x rearrange as
x^2 - 23x + 126 = 0 factor as
(x -9) (x -14) = 0
The second factor set to 0 gives us Amy's number
x - 14 = 0
x = 14
And Ben's number = y = 126/14 = 9
So 14 - 9 = 5
