How many whole numbers are there between 48 and 352 which are exactly divisible by 7?

Options

A. a)42
B. b)43
C. c)44
D. d)45

Answer

To find the number of whole numbers between 48 and 352 that are exactly divisible by 7, we can follow these steps:

### Step 1: Identify the first whole number greater than 48 that is divisible by 7.
To find this, we divide 48 by 7:
\[ 48 \div 7 = 6.857 \quad (\text{approximately}) \]
The next whole number after 6 is 7. Therefore, we multiply 7 by 7 to find the first multiple of 7:
\[ 7 \times 7 = 49 \]
So, the first number greater than 48 that is divisible by 7 is **49**.

### Step 2: Identify the largest whole number less than 352 that is divisible by 7.
Next, we divide 352 by 7:
\[ 352 \div 7 = 50.2857 \quad (\text{approximately}) \]
The largest whole number less than 50.2857 is 50. Therefore, we multiply 7 by 50 to find the largest multiple of 7:
\[ 7 \times 50 = 350 \]
So, the largest number less than 352 that is divisible by 7 is **350**.

### Step 3: List the sequence of numbers divisible by 7 between 49 and 350.
The numbers divisible by 7 form an arithmetic sequence where:
- The first term \( a = 49 \)
- The last term \( l = 350 \)
- The common difference \( d = 7 \)

### Step 4: Use the formula for the nth term of an arithmetic sequence.
The nth term of an arithmetic sequence can be calculated using the formula:
\[ l = a + (n-1) \cdot d \]
Substituting the known values:
\[ 350 = 49 + (n-1) \cdot 7 \]

### Step 5: Solve for \( n \).
First, subtract 49 from both sides:
\[ 350 - 49 = (n-1) \cdot 7 \]
\[ 301 = (n-1) \cdot 7 \]
Now, divide both sides by 7:
\[ n-1 = \frac{301}{7} = 43 \]
Adding 1 to both sides gives:
\[ n = 44 \]

### Conclusion:
Thus, the total number of whole numbers between 48 and 352 that are exactly divisible by 7 is **44**.

---