From the equation $c = 3$, we know that $b + c = 5$ becomes $b + 3 = 5$.
Solving for $b$, we find $b = 2$.
Substituting the values of $b$ and $c$ into the equation $a + b = c$, we have $a + 2 = 3$.
Solving for $a$, we find $a = 1$.
Therefore, the value of $a$ is $\boxed{1}$.The answer is: 1
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Given that $a + b = c$, $b + c = 5$, and $c = 3$, what is the value of $a$?

### Answer:
