Question

If the average of \(15, 25, 19, 20, 23, 18\) and\( (x-3)\) is \(20\). then Find the average of \(x, (x+6), (2x-1)\) and \(23\).

• A. \(20\)
• B. \(27\)
• C. \(28\frac{1}{2}\)
• D. \(30\)

Answer 1

The Correct Option is D

The average of the numbers 15, 25, 19, 20, 23, 18, and (x - 3) is given as 20. To find x, we use the formula for average:  \(\text{Average} = \frac{\text{Sum of terms}}{\text{Number of terms}}\).
Substituting the values, we have:
\[\frac{15 + 25 + 19 + 20 + 23 + 18 + (x-3)}{7} = 20\]
Simplifying the sum of terms:
\(15 + 25 + 19 + 20 + 23 + 18 = 120\)
Now substitute:
\[\frac{120 + (x-3)}{7} = 20\]
\[\frac{117 + x}{7} = 20\]
Multiply both sides by 7:
\(117 + x = 140\)
Solve for x:
\(x = 140 - 117 = 23\)
Next step is to find the average of x, (x+6), (2x-1), and 23. Substituting x = 23 into these terms:
x = 23
(x + 6) = 29
(2x - 1) = 45
The terms are 23, 29, 45, and 23. Calculate their average:
\[\text{Average} = \frac{23 + 29 + 45 + 23}{4}\]
Sum = 120
\[\text{Average} = \frac{120}{4} = 30\]

The average is \(30\).