Average of four numbers is 45.5. Third number is 250% more than the second number and fourth number is 41 less than third number. If first number is 15, then find the sum of second and fourth number.

Options

A. A)76
B. B)81
C. C)60
D. D)67

Answer

To solve the problem step by step, we will follow the information given in the question.

### Step 1: Understand the average
The average of four numbers is given as 45.5. Therefore, the sum of these four numbers can be calculated as:
\[ \text{Sum} = \text{Average} \times \text{Number of terms} = 45.5 \times 4 = 182 \]

**Hint:** Remember that the average is the total sum divided by the number of items.

### Step 2: Define the variables
Let the four numbers be:
- First number (A) = 15 (given)
- Second number (B) = unknown
- Third number (C) = unknown
- Fourth number (D) = unknown

### Step 3: Express C in terms of B
The third number (C) is 250% more than the second number (B). To express this mathematically:
\[ C = B + 2.5B = 3.5B \]

**Hint:** 250% more means you take the original amount and add 2.5 times that amount to it.

### Step 4: Express D in terms of C
The fourth number (D) is 41 less than the third number (C):
\[ D = C - 41 = 3.5B - 41 \]

**Hint:** When something is "less than" another value, you subtract that amount from it.

### Step 5: Set up the equation for the sum
Now we can express the total sum of the four numbers:
\[ A + B + C + D = 182 \]
Substituting the known values and expressions:
\[ 15 + B + 3.5B + (3.5B - 41) = 182 \]

### Step 6: Simplify the equation
Combine like terms:
\[ 15 + B + 3.5B + 3.5B - 41 = 182 \]
This simplifies to:
\[ 15 + 8B - 41 = 182 \]
\[ 8B - 26 = 182 \]

### Step 7: Solve for B
Add 26 to both sides:
\[ 8B = 182 + 26 \]
\[ 8B = 208 \]
Now divide by 8:
\[ B = \frac{208}{8} = 26 \]

**Hint:** When isolating a variable, perform the same operation on both sides of the equation.

### Step 8: Calculate C and D
Now that we have B, we can find C and D:
\[ C = 3.5B = 3.5 \times 26 = 91 \]
\[ D = C - 41 = 91 - 41 = 50 \]

### Step 9: Find the sum of B and D
Now we need to find the sum of the second number (B) and the fourth number (D):
\[ B + D = 26 + 50 = 76 \]

### Conclusion
The sum of the second and fourth numbers is:
\[ \boxed{76} \]