To solve this problem, we need to determine the number of broken medium mirrors that were shipped. Here’s a detailed step-by-step approach to find the solution:
1. Identify the missing values in the table:
- Small mirrors: We know that 4 mirrors were broken and the total number was 102. The table doesn't provide the number of not broken small mirrors, but it isn't required to solve the problem.
- Medium mirrors: The table indicates 6 mirrors were broken and 96 were not broken, but we need the total number of medium mirrors.
- Large mirrors: The table provides that 402 mirrors were not broken out of a total of 480.
2. Calculate the total number of broken mirrors:
- For small mirrors, there are 4 broken mirrors.
- For medium mirrors, there are 6 broken mirrors.
- For large mirrors:
[tex]\[
\text{Total large mirrors} - \text{Not broken large mirrors} = 480 - 402 = 78 \text{ broken large mirrors}
\][/tex]
3. Calculate the total number of medium mirrors:
- The total number of medium mirrors is the sum of broken and not broken medium mirrors:
[tex]\[
\text{Total medium mirrors} = \text{Broken medium} + \text{Not broken medium} = 6 + 96 = 102
\][/tex]
4. Sum up the total broken mirrors:
- Total broken mirrors for all sizes:
[tex]\[
\text{Total broken} = \text{Broken small mirrors} + \text{Broken medium mirrors} + \text{Broken large mirrors}
\][/tex]
[tex]\[
= 4 + 6 + 78 = 88
\][/tex]
Now, specifically for the medium mirrors:
- We were given that 6 medium mirrors were broken.
Hence, the number of broken medium mirrors shipped is:
- 6
Therefore, the correct answer is 6.
