The median of the numbers \(18, 21, 25, 27, 2x-1, 3x-6, 45, 48, 51, 57\) given in ascending order is 34. What is the value of \(x\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 15
The median of an even number of values in ascending order is the average of the two middle values. With 10 numbers, these are the 5th and 6th, here \(2x-1\) and \(3x-6\), so their average is set equal to 34:
Average of the 5th and 6th values: \(\displaystyle \frac{(2x-1)+(3x-6)}{2}=34\)
Solving: \(5x-7=68\), so \(x=15\)