Linear Equations

Let the number be , where is the tens digit and is the ones digit.
Step 1: According to the problem, the sum of the digits is 9, so:
Step 2: When 27 is added to the number, the digits are reversed. So, we have the equation:
Step 3: Simplify the equation:
Step 4: Solve the system of equations: 1. 2. Add both equations: Substitute into : Thus, the number is .

Let the number of prizes of Rs. 100 be , and the number of prizes of Rs. 50 be .
Step 1: The total amount spent on the prizes is:
Step 2: Simplify the equation:
Step 3: Solve for : Thus, the number of prizes of Rs. 100 is 40.