If a/3 = b/4 = c/7 (where a, b, c are non-zero), then the value of (a + b + c)…

When several quantities are given as equal ratios, such as a/3 = b/4 = c/7, introduce a single proportionality constant k so each variable can be written as a multiple of k. This converts the ratio equation into ordinary algebra with one variable instead of three.

1. Let a/3 = b/4 = c/7 = k, with k nonzero (so c ≠ 0).

2. Then a = 3k, b = 4k, and c = 7k.

3. Substitute into the expression (a + b + c)/c: (3k + 4k + 7k)/7k = 14k/7k.

4. Cancel k: 14k/7k = 2.

Cross-check with k = 1: a = 3, b = 4, c = 7, so a + b + c = 14 and 14/7 = 2 - the same result, confirming the value is independent of k (for any nonzero k).

Hence (a + b + c)/c = 2.