Three positive numbers are in the ratio 7:3:2. The sum of the smallest number to the largest number exceeds twice the remaining number by 30. Find the three numbers.

The numbers are 70,30,20.

Step-by-step explanation:

Let the three numbers be 7x, 3x and 2x.

The sum of smallest and largest number is 7x+2x=9x.

According to question:

9x-30=2 (3x)

Simplifying the equation:

9x-30=6x

Adding 30 both sides:

9x=6x+30 or, 9x-6x=30

3x=30, x=10,

The numbers are 7x=7 (10) = 70

3x=3 (10) = 30

2x=2 (10) = 20.