Write down the given ages and the mean.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Write down the given ages and the mean.
The ages are $8, 11, 8, 10, 5, 7, 2u, 11, 11$.
The number of ages is $n=9$.
The mean age is $9$ years.
Step 2: Use the formula for the mean.
The mean is the sum of all values divided by the number of values.
$$ \text{Mean} = \frac{\sum \text{ages}}{n} $$
Step 3: Substitute the given values into the mean formula.
$$ 9 = \frac{8 + 11 + 8 + 10 + 5 + 7 + 2u + 11 + 11}{9} $$
Step 4: Sum the known numerical values in the numerator.
$$ 8 + 11 + 8 + 10 + 5 + 7 + 11 + 11 = 71 $$
So the equation becomes:
$$ 9 = \frac{71 + 2u}{9} $$
Step 5: Solve for $u$.
Multiply both sides by $9$:
$$ 9 \times 9 = 71 + 2u $$
$$ 81 = 71 + 2u $$
Subtract $71$ from both sides:
$$ 81 - 71 = 2u $$
$$ 10 = 2u $$
Divide by $2$:
$$ u = \frac{10}{2} $$
$$ u = 5 $$
The value of $u$ is $\boxed{\text{5}}$.
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