Two numbers are in the ratio 5 to 9. If 5 is subtracted from each number, the new ratio becomes 5 to 11. What are the original numbers?

Explanation

Let the two numbers be 5x and 9x. According to the problem, (5x - 5) / (9x - 5) = 5 / 11. Cross-multiplying gives 11(5x - 5) = 5(9x - 5), which simplifies to 55x - 55 = 45x - 25. Solving for x, we get 10x = 30, so x = 3. Therefore, the original numbers are 5 * 3 = 15 and 9 * 3 = 27.