Of the four numbers whose average is 60 , the first is `(1)/(4)` th of the sum of the last three . The first number is

Options

A. 15
B. 45
C. 48
D. 60. 25

Answer

To find the first number in the problem, we can follow these steps:

### Step 1: Understand the average
The average of four numbers is given as 60. The formula for the average is:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Number of items}} \]
In this case, we have:
\[ 60 = \frac{a + b + c + d}{4} \]
Where \( a, b, c, d \) are the four numbers.

### Step 2: Calculate the sum of the numbers
To find the sum of the four numbers, we can rearrange the formula:
\[ a + b + c + d = 60 \times 4 = 240 \]
So, the sum of the four numbers is 240.

### Step 3: Express the first number in terms of the other three
We are told that the first number \( a \) is \( \frac{1}{4} \) of the sum of the last three numbers \( b, c, d \). This can be expressed as:
\[ a = \frac{1}{4}(b + c + d) \]

### Step 4: Substitute the sum of the last three numbers
From the total sum, we can express \( b + c + d \) as:
\[ b + c + d = 240 - a \]
Now, substituting this into the equation for \( a \):
\[ a = \frac{1}{4}(240 - a) \]

### Step 5: Solve for \( a \)
Now we can solve for \( a \):
\[ a = \frac{240 - a}{4} \]
Multiplying both sides by 4 to eliminate the fraction:
\[ 4a = 240 - a \]
Now, add \( a \) to both sides:
\[ 4a + a = 240 \]
\[ 5a = 240 \]
Now, divide both sides by 5:
\[ a = \frac{240}{5} = 48 \]

### Conclusion
The first number \( a \) is 48.

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