1. **State the problem:** We are given the equation $C = b - a$ with $a = 6$ (correct to the nearest integer) and $b = 15$ (correct to the nearest 5). We need to find the upper bound for $C$. 2. **Understand the bounds:** - Since $a$ is correct to the nearest integer, $a$ can be as low as $5.5$ and as high as $6.5$. - Since $b$ is correct to the nearest 5, $b$ can be as low as $12.5$ and as high as $17.5$. 3. **Formula for upper bound:** The upper bound for $C = b - a$ is when $b$ is at its maximum and $a$ is at its minimum: $$C_{upper} = b_{max} - a_{min}$$ 4. **Calculate upper bound:** $$C_{upper} = 17.5 - 5.5 = 12$$ 5. **Final answer:** The upper bound for $C$ is $12$.