c) The sum of two numbers is 200. Dividing the first by 12 and the second by 10, the sum of these quotients is 18. What are the numbers?

x + y = 200
\frac{x}{12} + \frac{y}{10} = 18

To solve:
1. Solve for \( y \) from the first equation and substitute in the second:
y = 200 - x
\frac{x}{12} + \frac{200 - x}{10} = 18

2. Clear the denominators by multiplying through by 60:
5x + 6(200 - x) = 1080
5x + 1200 - 6x = 1080
-x + 1200 = 1080

3. Solve for \( x \):
-x = 1080 - 1200
-x = -120
x = 120

4. Find \( y \):
y = 200 - x
y = 200 - 120
y = 80

Hence, the numbers are:
x = 120, \quad y = 80