The volume of substance A is half the sum of the volumes of substances B and C, and the volume of substance B is 20%

The volume of substance A is half the sum of the volumes of substances B and C, and the volume of substance B is 20% of the sum of the volumes of substances A and C. Find the ratio of the volume of substance C to the sum of the volumes of substances A and B.

Let us denote the volume of each substance by the corresponding letter, then the condition of the problem can be written as follows:

A = (B + C) / 2,

B = (A + C) / 5.

From the first equation we get B = 2 * A – C, and from the second equation A = 5 * B – C.

Let us express A and B through C.

B = 2 * (5 * B – C) – C = 10 * B – 3 * C, which means 9 * B = 3 * C, that is

B = C / 3.

A = 5 * (2 * A – C) – C = 10 * A – 6 * C, which means A = 2 * C / 3.

Thus, we get:

A + B = C / 3 + 2 * C / 3 = C.

Therefore, (A + B) / C = 1.