Information about a shipment of mirrors to a local store is shown.
| | Broken | Not Broken | Total |
| :----- | :----- | :--------- | :---- |
| Small | 4 | | 102 |
| Medium | | 96 | |
| Large | 6 | | 214 |
| Total | | 402 | 480 |
For all of the medium mirrors that were shipped, how many of them were broken?
Answer (2)
Calculate the number of not broken small mirrors: 102 − 4 = 98 .
Calculate the number of not broken large mirrors: 214 − 6 = 208 .
Calculate the total number of medium mirrors: 480 − 102 − 214 = 164 .
Calculate the number of broken medium mirrors: $164 - 96 = \boxed{68}.
Explanation
Understand the problem We are given a table with information about a shipment of mirrors. The table categorizes the mirrors by size (small, medium, large) and condition (broken, not broken). We need to find the number of broken medium mirrors.
Calculate not broken small mirrors First, let's find the number of 'Not Broken' small mirrors. We know there are a total of 102 small mirrors and 4 are broken. So, the number of small mirrors that are not broken is:
102 − 4 = 98
Calculate not broken large mirrors Next, let's find the number of 'Not Broken' large mirrors. We know there are a total of 214 large mirrors and 6 are broken. So, the number of large mirrors that are not broken is:
214 − 6 = 208
Calculate total medium mirrors Now, let's find the total number of medium mirrors. We know the total number of mirrors is 480, and we have 102 small mirrors and 214 large mirrors. So, the number of medium mirrors is:
480 − 102 − 214 = 164
Calculate broken medium mirrors Finally, let's find the number of broken medium mirrors. We know there are 164 total medium mirrors and 96 are not broken. So, the number of broken medium mirrors is:
164 − 96 = 68
State the final answer Therefore, the number of broken medium mirrors is 68.
Examples
This type of problem is useful in inventory management and quality control. For example, a store manager might use a similar table to track damaged goods and identify patterns in shipping or handling that lead to breakage. By analyzing the data, they can make informed decisions about packaging, transportation, or storage to minimize losses.
The number of broken medium mirrors is 68. This is determined by calculating the total medium mirrors and subtracting the number of non-broken medium mirrors. Steps include finding not broken small and large mirrors, and using those totals to find the medium mirrors.
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