Final answer:
The smaller number is 44 and the larger number is 160.
Step-by-step explanation:
Let's represent the smaller number as 'x' and the larger number as 'y'.
According to the problem, the sum of the two integers is 208, so we can write the equation: x + y = 208.
The larger number is 32 more than 3 times the smaller number, which can be represented as: y = 3x + 32.
Substituting the value of y from the second equation into the first equation, we get: x + (3x + 32) = 208.
Simplifying the equation, we have: 4x + 32 = 208.
Subtracting 32 from both sides, we get: 4x = 176.
Dividing both sides by 4, we find that x = 44.
Substituting the value of x back into the second equation, we find that y = 3(44) + 32 = 160.
Therefore, the two numbers are 44 and 160.