The sum of two numbers is 12. When three times the first number is added to 5 times the second number, the resultant number is 44. What are the two numbers?

Let's denote the first number as x and the second number as y.

From the problem, we have two equations:

1. x + y = 12 (since the sum of two numbers is 12)

2. 3x + 5y = 44 (since when three times the first number is added to five times the second number, the resultant number is 44)

We can solve these equations step by step:

Step 1: Solve the first equation for x: x = 12 - y

Step 2: Substitute x in the second equation: 3(12 - y) + 5y = 44

Step 3: Simplify the equation: 36 - 3y + 5y = 44

Step 4: Combine like terms: 2y = 44 - 36

Step 5: Solve for y: y = 8 / 2 = 4

Step 6: Substitute y = 4 in the first equation: x + 4 = 12

Step 7: Solve for x: x = 12 - 4 = 8

So, the two numbers are 8 and 4.