Two numbers have a highest common factor (HCF) of 5 and a least common multiple (LCM) of 495. If their sum is 100, what is the difference between the two numbers?

Explanation

Let the two numbers be x and (100 - x). Since their product equals the product of their HCF and LCM, we have x * (100 - x) = 5 * 495 = 2475. This leads to the quadratic equation x^2 - 100x + 2475 = 0. Factoring gives (x - 55)(x - 45) = 0, so the numbers are 45 and 55. The difference is 55 - 45 = 10.