To solve this problem, we can set up a system of equations.

Letβs assume the three numbers are A, B, and C.

According to the given ratio, we can write the following equations:

A/B = 1/3 B/C = 2/3 A/C = 3/4

We can rewrite these equations as:

A = (1/3)B B = (3/2)C A = (3/4)C

Now, we can substitute the values of A and B in terms of C into the equation A + B + C = 276:

(1/3)B + B + (3/2)C + C = 276

Multiplying through by 6 to eliminate the fractions, we get:

2B + 6B + 9C + 6C = 1656

Combining like terms, we have:

8B + 15C = 1656

Since we have two equations with two variables (A and B), we can solve for B and C.

From the equation B = (3/2)C, we can substitute this into the equation 8B + 15C = 1656:

8((3/2)C) + 15C = 1656 12C + 15C = 1656 27C = 1656 C = 1656/27 C β 61.33

Now, we can substitute the value of C back into the equation B = (3/2)C to find B:

B = (3/2)(61.33) B β 91.99

Finally, we can substitute the values of B and C into the equation A = (1/3)B to find A:

A = (1/3)(91.99) A β 30.66

Therefore, the three numbers are approximately 30.66, 91.99, and 61.33, which are not the same as the given answer of 72, 96, and 108. It seems there may be an error in the given answer.