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?

Nerdo Apr 10, 2020

#1**+5 **

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

CPhill Apr 10, 2020