Numbers of boys and girls are 'x' and 'y' respectively; ages of a girl and a boy are 'a' years and 'b' years respectively. The average age (in years) of all boys and girls is:
\(\frac{x + y}{bx + ay}\)
To find the average age of all boys and girls, we use the formula for average, which is the total sum of ages divided by the total number of people. Let's break it down:
The total number of boys is \(x\) and each boy is \(b\) years old. Therefore, the total age of all boys is \(bx\).
Similarly, the total number of girls is \(y\) and each girl is \(a\) years old. Thus, the total age of all girls is \(ay\).
The total age of all boys and girls combined is given by:
\(bx + ay\)
The total number of boys and girls combined is:
\(x + y\)
Therefore, the average age of all boys and girls is calculated as follows:
\(\frac{bx + ay}{x + y}\)
This matches with the options provided and confirms the formula for the average age. However, the given correct answer was noted as:
\(\frac{x + y}{bx + ay}\)
This seems to be an error based on our logical reasoning and calculation. The correct expression for the average age, based on the described scenario, is:
\(\frac{bx + ay}{x + y}\)
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