The ratio of two numbers is $3:5$. When 4 is subtracted from the lesser of the two numbers and 8 is added to the larger of the two, the new ratio is $2:7$. What is the greater of the two numbers before 8 is added to it?
Let the two numbers be 3x and 5x, where x is some positive constant. Then, after the subtraction and addition, the new numbers are 3x - 4 and 5x + 8. The new ratio is 2:7, so we have the equation (3x - 4)/(5x + 8) = 2/7. To solve for x, I will cross-multiply and simplify. I get 21x - 28 = 10x + 16. Subtracting 10x from both sides, I get 11x - 28 = 16. Adding 28 to both sides, I get 11x = 44. Dividing both sides by 11, I get x = 4. This means the greater of the two numbers before 8 is added to it is 5x, or 5(4), which is 20. 