Final answer:
To find the three numbers in the ratio 7:3:2, we can use algebraic equations. Solving the equation that represents the given condition, we find that the three numbers are 70, 30, and 20.
Step-by-step explanation:
To solve this problem, we can represent the three numbers in the ratio as 7x, 3x, and 2x, where x is a common factor. The given condition is that the sum of the least number and the greatest number exceeds twice the remaining number by 30. In equation form, this can be written as:
7x + 2x = 2(3x) + 30
Simplifying this equation, we get:
7x + 2x = 6x + 30
9x = 6x + 30
Subtracting 6x from both sides, we have:
3x = 30
Dividing both sides by 3, we find that x = 10. Therefore, the three numbers are:
7x = 7(10) = 70
3x = 3(10) = 30
2x = 2(10) = 20
So the three numbers are 70, 30, and 20.