What is the sum of three numbers if the first number refers to the second as 2: 3

What is the sum of three numbers if the first number refers to the second as 2: 3, the second to the third as 5: 6, and the ratio of the largest number and the smallest number is 8?

Let us assume that the 1st, 2nd and 3rd numbers are A1, A2 and A3.

Then it is known that A1 / A2 = 2/3, A2 / A3 = 5/6, A3 – A1 = 8.

A2 = 3/2 * A1.

A3 = 6/5 * A2 = 6/5 * 3/2 * A1 = 9/5 * A1.

9/5 * A1 – A1 = 8.

4/5 * A1 = 8.

A1 = 8 * 5/4.

A1 = 10.

A3 = A1 + 8 = 10 + 8 = 18.

A2 = 3/2 * A1 = 3/2 * 10 = 15.

A1 + A2 + A3 = 10 + 15 + 18 = 43.

Answer: The sum of the three numbers is 43.