Among three numbers, the first is twice the second and thrice the third. If…

Step-by-Step Solution

To solve this, we express the three numbers in terms of a single variable based on the provided relationships.

1. Define the variables:

   • Let the first number be 6x (this allows it to be divisible by both 2 and 3).

   • Since the first number (6x) is twice the second, the second number is 6x / 2 = 3x.

   • Since the first number (6x) is thrice the third, the third number is 6x / 3 = 2x.

2. Use the average to find x:

   • The average of the three numbers is 506.

   • (6x + 3x + 2x) / 3 = 506

   • 11x / 3 = 506

   • 11x = 1518

   • x = 1518 / 11 = 138.

3. Calculate the numbers and their difference:

   • The first number is 6 * 138 = 828.

   • The third number is 2 * 138 = 276.

   • The difference between the first and third numbers is 828 - 276 = 552.