What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion?354-3

To find the number that must be added to each of the numbers 7, 11, and 19 so that the resulting numbers are in continued proportion, we need to follow these steps:

1. Let's denote the number to be added as x. So, the three numbers in continued proportion would be 7+x, 11+x, and 19+x.

2. In a continued proportion, the product of the first and third terms is equal to the square of the second term. So, we can set up the equation: (7+x)*(19+x) = (11+x)^2.

3. Expanding and simplifying this equation gives: 133 + 26x + x^2 = 121 + 22x + x^2.

4. By subtracting the like terms on both sides, we get: 12 = 4x.

5. Solving for x, we find that x = 3.

So, the number that must be added to each of the numbers 7, 11, and 19 so that the resulting numbers are in continued proportion is 3.