Question

The sum of two positive numbers is 55 times their difference. What is the ratio of the larger number to the smaller number?

Answer 1

Hello,

Let's assume
a the largest number
b the smallest. not equal 0

a+b=55(a-b)
==>a/b+1=55a/b-55
==>a/b-55a/b=-56
==>-54 a/b=-56
==>a/b=56/54
==>a/b=28/27

Answer 2

$x;y\in\mathbb{R^+}-two\ positive\ numbers\ (x \ \textgreater \ 0\ and\ y \ \textgreater \ 0)\\x \ \textgreater \ y\\\\x+y=55(x-y)\\\\x+y=55x-55y\ \ \ \ |subtract\ "y"\ from\ both\ sides\\\\x=55x-56y\ \ \ \ |subtract\ 55x\ from\ both\ sides\\\\-54x=-56y\ \ \ |divide\ both\ sides\ by\ (-54)\\\\x=\dfrac{-56y}{-54}\\\\x=\dfrac{28}{27}y\ \ \ \ |divide\ both\ sides\ by\ "y"\\\\\boxed{\dfrac{x}{y}=\dfrac{28}{27}}\to\boxed{x:y=28:27}$