Abe reads a book every day some page in the morning and some in the evening. He reads 23 pages every morning and 31 page every evening . The number of page completed by Abe after some number of days can be written as a function of the number of pages read in the evening . If the number of days is represented by ' N', the number of page read in the morning be 'M' and the number of pages read in the evenings be 'E' , which of the following the number of days for which Abe read the book ? It is know that if Abe read in the morning , he did not read in the evening and vice versa.

Options

A. N = 23M + 31E
B. N = 31M + 23E
C. `N = (M)/(23) + (E)/(31)`
D. `N = (M)/(31) + (E)/(23)`

Answer

To solve the problem step by step, we will derive the total number of days Abe read the book based on the pages he read in the morning and evening.

### Step 1: Define Variables
Let:
- \( N \) = Total number of days Abe read the book
- \( M \) = Total number of pages read in the morning
- \( E \) = Total number of pages read in the evening

### Step 2: Determine Pages Read Per Day
Abe reads:
- 23 pages every morning
- 31 pages every evening

### Step 3: Calculate Days Based on Morning Reading
If Abe reads in the morning, the number of days he read in the morning can be calculated as:
\[ \text{Number of days reading in the morning} = \frac{M}{23} \]
This is because he reads 23 pages each day, so the total pages read in the morning \( M \) divided by 23 gives the number of days.

### Step 4: Calculate Days Based on Evening Reading
Similarly, if Abe reads in the evening, the number of days he read in the evening can be calculated as:
\[ \text{Number of days reading in the evening} = \frac{E}{31} \]
This is because he reads 31 pages each evening, so the total pages read in the evening \( E \) divided by 31 gives the number of days.

### Step 5: Total Days Calculation
Since Abe reads either in the morning or in the evening on any given day, the total number of days \( N \) he read the book can be expressed as:
\[ N = \left(\frac{M}{23}\right) + \left(\frac{E}{31}\right) \]

### Conclusion
Thus, the formula for the total number of days Abe read the book is:
\[ N = \frac{M}{23} + \frac{E}{31} \]