Information about a shipment of mirrors to a local store is shown.

\begin{tabular}{|c|c|c|c|}
\hline
& Broken & \begin{tabular}{c}
Not \\
Broken
\end{tabular} & Total \\
\hline
Small & 4 & 98 & 102 \\
\hline
Medium & 6 & 96 & 102 \\
\hline
Large & 78 & 402 & 480 \\
\hline
Total & 88 & 596 & 684 \\
\hline
\end{tabular}

Of all of the medium mirrors that were shipped, how many of them were broken?

A. 68
B. 78
C. 164
D. 208



Answer :

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.