The average of numbers N1 and N2 is 17. The average of numbers N2 and N3 is 44. What is the difference between N3 and N1?

Options

A. 54
B. 35
C. 27
D. 36

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Set up the equations based on the averages given.
We know that the average of numbers \( N1 \) and \( N2 \) is 17. This can be expressed as:
\[ \frac{N1 + N2}{2} = 17 \]
Multiplying both sides by 2 gives us:
\[ N1 + N2 = 34 \quad \text{(Equation 1)} \]

### Step 2: Set up the second equation.
We also know that the average of numbers \( N2 \) and \( N3 \) is 44. This can be expressed as:
\[ \frac{N2 + N3}{2} = 44 \]
Multiplying both sides by 2 gives us:
\[ N2 + N3 = 88 \quad \text{(Equation 2)} \]

### Step 3: Subtract Equation 1 from Equation 2.
Now, we will subtract Equation 1 from Equation 2 to find the difference between \( N3 \) and \( N1 \):
\[ (N2 + N3) - (N1 + N2) = 88 - 34 \]
This simplifies to:
\[ N3 - N1 = 54 \]

### Step 4: Conclusion.
Thus, the difference between \( N3 \) and \( N1 \) is:
\[ N3 - N1 = 54 \]

### Final Answer:
The difference between \( N3 \) and \( N1 \) is 54.

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