Explanation

Given information:

1. The average of the first three numbers (A, B, C) is 15

   $$frac{A + B + C}{3} = 15$$ $$A + B + C = 45$$

2. The average of the last three numbers (B, C, D) is 16

   $$frac{B + C + D}{3} = 16$$ $$B + C + D = 48$$

3. The last number (D) is 19

   $$B + C + 19 = 48$$ $$B + C = 29$$

Finding A

We already have:

$$A + B + C = 45$$

Substituting $B + C = 29$:

$$A + 29 = 45$$$$A = 45 - 29$$ $$A = 16$$