MON  TUE  WED  THU   FRI

 49      73     50     63     85

 88      20     35     34     75

MON  TUE   WED  THU  FRI 

 68      43      67      78    66

 10       14      25      12     72

MON   TUE  WED   THU  FRI 

  77       36     63     00     00

  44       01     97      63     44

MON  TUE   WED   THU  FRI 

  91       13      51      76     31

  34      36      15      85    97

MON    TUE   WED   THU  FRI 

09        29      54       57     83

30        03      78       48     =?

Please solve the question?




To solve the question, we need to figure out the missing number in the last grid for Friday (Fifth row, fifth column).

Let's analyze each of the previous rows for patterns. The data seems to be grouped in pairs:

```
MON   TUE   WED   THU   FRI
--------------------------------
 49      73     50     63     85
 88      20     35     34     75
--------------------------------
 68      43     67     78     66
 10      14     25     12     72
--------------------------------
 77      36     63     00     00
 44      01     97     63     44
--------------------------------
 91      13     51     76     31
 34      36     15     85     97
--------------------------------
 09      29     54     57     83
 30      03     78     48     =?
```

Looking at the pairs of numbers in each row for each day:

1. **Friday (Column 5)**:
   - (85, 75), (66, 72), (00, 44), (31, 97)
   - The sum of each pair in Friday gives:
     - 85 + 75 = 160
     - 66 + 72 = 138
     - 00 + 44 = 44
     - 31 + 97 = 128

We observe that there is no fixed pattern in sums. However, we might consider that the missing number could follow the sum trend, where Friday's numbers (83, ?) should add up to match the rough range of previous sums.

- The previous sums ranged from 44 to 160. So:
  - If the missing number is "x", then \( 83 + x \) should reasonably fall within this range.

To maintain consistency with the other sums, we might assume that \( 83 + x \approx 128 \), similar to (31, 97) pair.

So:
\[
83 + x = 128
\]
\[
x = 128 - 83 = 45
\]

Thus, the missing number is **45**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What other patterns can you observe from the data?
2. How could this approach differ if the pattern was multiplicative instead of additive?
3. What other methods could be used to solve for missing numbers in sequences?
4. How would you calculate sums across multiple columns or rows in large datasets?
5. What might change if there were negative numbers in the grid?

**Tip**: Always look for relationships between rows or columns when analyzing grids or sequences!

MON  TUE  WED  THU   FRI

49      73     50     63     85
88      20     35     34     75

MON  TUE   WED  THU  FRI 
68      43     67     78    66
10      14     25     12     72

MON   TUE  WED   THU  FRI 
77       36     63     00     00
44       01     97      63     44

MON  TUE   WED   THU  FRI 
91       13      51      76     31
34      36      15      85    97

MON    TUE   WED   THU  FRI 
09        29      54       57     83
30        03      78       48     =?

Please solve the question?

Discover how to solve for the missing number in a grid pattern involving days of the week. Learn how sums of pairs were analyzed to find the missing value for Friday, with detailed calculations and pattern recognition strategies. Suitable for Grades 6-8.

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