If $A : B = 5 : 6$ and $B : C = 6 : 7$, then find the ratio $A + B : B + C : A + C$.

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**Solution:**

1. Given ratios:
   - $A : B = 5 : 6$
   - $B : C = 6 : 7$

2. Since $B$ is common in both ratios and equal to 6 in both, we can directly use these values.

3. Calculate the sums:
   - $A + B = 5 + 6 = 11$
   - $B + C = 6 + 7 = 13$
   - $A + C = 5 + 7 = 12$

4. Therefore, the ratio $A + B : B + C : A + C = 11 : 13 : 12$

**Answer:** $11 : 13 : 12$

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