average

The average score of the last 3 quizzes of Sofia was 83. The overall average of her 6 quizzes was 86. What was her average score for the first 3 quizzes?

$\begin{array}{rcl} \frac{s_1+s_2+s_3}{3} &=& ? \\ \hline \frac{s_4+s_5+s_6}{3} &=& 83 \qquad | \qquad \cdot \frac12\\\\ \frac{s_4+s_5+s_6}{6} &=& \frac{83}{2}\\ \hline \frac{s_1+s_2+s_3+s_4+s_5+s_6}{6} &=& 86 \\ \frac{s_1+s_2+s_3}{6} + \frac{s_4+s_5+s_6}{6} &=& 86 \\ \frac{s_1+s_2+s_3}{6} + \frac{83}{2} &=& 86 \qquad | \qquad \cdot 2 \\ \frac{s_1+s_2+s_3}{3} + 83 &=& 86 \cdot 2 \\ \frac{s_1+s_2+s_3}{3} + 83 &=& 172\\ \frac{s_1+s_2+s_3}{3} &=& 172 - 83 \\ \mathbf{\frac{s_1+s_2+s_3}{3}} & \mathbf{=} & \mathbf{89} \\ \end{array}$

The average score for the first 3 quizzes was 89