Final answer:
The first number is 36, the second number is 180, and the third number is 136.
Step-by-step explanation:
Let's denote the first number as x. The second number is 5 times the first number, so it can be expressed as 5x. The third number is 100 more than the first number, so it can be expressed as x + 100.
The sum of the three numbers is 352, so we can write the equation: x + 5x + (x + 100) = 352.
Combining like terms, we get 7x + 100 = 352.
Subtracting 100 from both sides, we have 7x = 252.
Dividing both sides by 7, we get x = 36.
Therefore, the first number is 36, the second number is 5 times 36, which is 180, and the third number is 36 + 100, which is 136.