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

let the numbers be a and b.  a is the larger of the two numbers. Sum = 55* Difference a + b =  55(a - b) a + b = 55a - 55b a - 55a = -55b - b -54a = -56b a/b = -56/-54    (From cross multiplication) a/b = 56/54  simplify out by 2. a/b = 28/27 Therefore the ratio of larger to smaller number = 28/27