If the arithmetic mean of 7, 13, 20, 17, and \( 3x \) is 18, then the value of \( x \) will be:
Show Hint
- 20
- 15
- 11
- 9
The Correct Option is B
Solution and Explanation
Step 1: Use the formula for the arithmetic mean.
The arithmetic mean is given by the formula: \[ \text{Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}} \] We are given that the arithmetic mean is 18, so: \[ 18 = \frac{7 + 13 + 20 + 17 + 3x}{5} \]
Step 2: Solve for \( x \).
First, find the sum of the known terms: \[ 7 + 13 + 20 + 17 = 57 \] Substitute this into the equation: \[ 18 = \frac{57 + 3x}{5} \] Multiply both sides by 5: \[ 90 = 57 + 3x \] Subtract 57 from both sides: \[ 33 = 3x \] Now divide by 3: \[ x = \frac{33}{3} = 11 \]
Step 3: Conclusion.
Thus, the value of \( x \) is 11. Therefore, the correct answer is (C).
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