The arithmetic mean of three numbers is 4.2. the first number is 1.2 times the second, 2.7 more than the third. find these numbers.

To find numbers that satisfy the condition that the arithmetic mean of three numbers is 4.2. The first number is 1.2 times the second, and 2.7 times the third.
Let’s use the variable x to denote the second number, then the first number can be written as 1.2x, and the third number looks like this 1.2x – 2.7.
Let’s write the arithmetic mean of these numbers:
(x + 1.2x + 1.2x – 2.7) / 3 = 4.2;
x + 1.2x + 1.2x – 2.7 = 12.6;
3.4x = 12.6 + 2.7;
3.4x = 15.3;
x = 15.3: 3.4;
x = 4.5 is the second number,
1.2 * 4.5 = 5.4 – the first number,
5.4 – 2.7 = 2.7 is the third number.