Final answer:
To find the three natural numbers, represent the first number by x, resulting in an equation x + (2x + 30) + (x - 10) = 220. Solving this gives the numbers as 50, 130, and 40.
Step-by-step explanation:
The student needs to find three natural numbers whose sum is 220. According to the given conditions, the second number is 30 more than twice the first number, and the third number is 10 less than the first number. To create an equation, let's denote the first number by x. The second number will then be 2x + 30 and the third number will be x - 10. The equation that represents the sum of these three numbers is:
x + (2x + 30) + (x - 10) = 220
Simplifying the equation, we have:
4x + 20 = 220
Subtracting 20 from both sides, we get:
4x = 200
Dividing both sides by 4, we find:
x = 50
Therefore, the first number is 50, the second number is 2(50) + 30 = 130, and the third number is 50 - 10 = 40. Thus, the three natural numbers are 50, 130, and 40.