Everyone's 81021

There are 10 students in the drama club. We count everyone's age in whole years. The average age of the girls is 12.25 and the boys 12.5, and the average age of all is 12.3. How many girls and how many boys are there in the class?

Correct answer:

a =  2
b =  8

Step-by-step explanation:

$$\begin{gathered} a+b=10 \\ 12.5\cdot a+12.25\cdot b=12.3\cdot 10 \\ a+b=10 \\ 12.5a+12.25b=123 \\ Pivot:Row1\leftrightarrow Row2 \\ 12.5a+12.25b=123 \\ a+b=10 \\ Row2-\frac{1}{12.5}\cdot Row1\to Row2 \\ 12.5a+12.25b=123 \\ 0.02b=0.16 \\ b=\frac{0.16}{0.02}=8 \\ a=\frac{123-12.25b}{12.5}=\frac{123-12.25\cdot 8}{12.5}=2 \\ a=2 \\ b=8 \end{gathered}$$

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