The total sales of regular and giant size boxes of detergent at two stores is given for three months.
    	    	Store	    	Store	    	Store	    
    	    	   1	2   	    	   1	2   	    	   1	2   	    
Regular	    	

85	46	

71	91
    	

89	62	

98	49
    	

57	47	

62	35
Giant
    	    	March	    	April	    	May	    
Use matrix arithmetic to find the average monthly sales by store and size. (Round your answers to two decimal places.) 
  	Store 1	  	Store 2
 Regular 
 Giant 


To find the average monthly sales by store and size using matrix arithmetic, we first organize the data into a matrix format.

Given dataTo find the average monthly sales by store and size using matrix arithmetic, we first organize the data into a matrix format.

Given 

|          | Store 1 | Store 2 |
|----------|---------|---------|
| **March** Regular | 85      | 46      |
| **March** Giant   | 71      | 91      |
| **April** Regular | 89      | 62      |
| **April** Giant   | 98      | 49      |
| **May** Regular   | 57      | 47      |
| **May** Giant     | 62      | 35      |

We will compute the average sales by:

1. Adding up the sales for each store for both regular and giant sizes across the three months.
2. Dividing the total by the number of months (3).

### Step 1: Summing up sales for each store

#### Store 1:
- **Regular**: \( 85 + 89 + 57 = 231 \)
- **Giant**: \( 71 + 98 + 62 = 231 \)

#### Store 2:
- **Regular**: \( 46 + 62 + 47 = 155 \)
- **Giant**: \( 91 + 49 + 35 = 175 \)

### Step 2: Calculating the average sales by dividing by 3 (number of months)

#### Store 1:
- **Regular**: \( \frac{231}{3} = 77.00 \)
- **Giant**: \( \frac{231}{3} = 77.00 \)

#### Store 2:
- **Regular**: \( \frac{155}{3} \approx 51.67 \)
- **Giant**: \( \frac{175}{3} \approx 58.33 \)

### Final Answer:

|          | Store 1 | Store 2  |
|----------|---------|----------|
| **Regular** | 77.00   | 51.67    |
| **Giant**   | 77.00   | 58.33    |

Would you like further details on how matrix arithmetic applies here, or any additional clarification?

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**Related Questions**:
1. How do you define matrix addition and scalar multiplication?
2. Can you show how to represent the given data as a matrix?
3. What are some common matrix operations in sales analysis?
4. How does matrix multiplication differ from scalar division in this context?
5. Can we solve this problem using Excel or other software tools?

**Tip**: Always verify that you are dividing by the correct number of entries when averaging data in matrices!

The total sales of regular and giant size boxes of detergent at two stores is given for three months. Store Store Store 1 2 Store Store Store 1 2 Store Store Store 1 2 Regular 85 46 71 91 89 62 98 49 57 47 62 35 Giant March April May Use matrix arithmetic to find the average monthly sales by store and size. (Round your answers to two decimal places.) Store 1 Store 2 Regular Giant

Use matrix arithmetic to calculate the average monthly sales of regular and giant detergent boxes across two stores over three months. This problem explores matrix data representation and summing values to compute averages, ideal for high school students. Example: Regular sales for Store 1 average 77.00, while Store 2 averages 51.67.

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