The average of the two-digit numbers 41, x5, 5x and 44 is 57. What is the average of (x+5) and (2x-9) ?

Options

A. 10
B. 13
C. 9
D. 11

Answer

To solve the problem step by step, we need to find the value of \( x \) first and then calculate the average of \( (x + 5) \) and \( (2x - 9) \).

### Step 1: Set up the equation for the average
We know that the average of the numbers \( 41, x5, 5x, \) and \( 44 \) is \( 57 \). The formula for the average is given by:

\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Total number of items}} \]

In this case, we have:

\[ \frac{41 + (10x + 5) + (50 + x) + 44}{4} = 57 \]

### Step 2: Simplify the equation
Now, we can simplify the equation. The sum of the numbers is:

\[ 41 + (10x + 5) + (50 + x) + 44 = 41 + 5 + 50 + 44 + 10x + x = 140 + 11x \]

So, we can rewrite the equation as:

\[ \frac{140 + 11x}{4} = 57 \]

### Step 3: Multiply both sides by 4
To eliminate the fraction, we multiply both sides by 4:

\[ 140 + 11x = 228 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \):

\[ 11x = 228 - 140 \]
\[ 11x = 88 \]
\[ x = \frac{88}{11} = 8 \]

### Step 5: Calculate \( (x + 5) \) and \( (2x - 9) \)
Now that we have \( x = 8 \), we can calculate \( (x + 5) \) and \( (2x - 9) \):

\[ x + 5 = 8 + 5 = 13 \]
\[ 2x - 9 = 2(8) - 9 = 16 - 9 = 7 \]

### Step 6: Find the average of \( (x + 5) \) and \( (2x - 9) \)
Now we find the average of \( 13 \) and \( 7 \):

\[ \text{Average} = \frac{(x + 5) + (2x - 9)}{2} = \frac{13 + 7}{2} = \frac{20}{2} = 10 \]

### Final Answer
The average of \( (x + 5) \) and \( (2x - 9) \) is \( 10 \).

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