Movie theatre

At the movie theatre, child admission is 5.40, and adult admission is 9.70. On Thursday, the theatre sold 159 tickets for a total sales of 1142.40. How many child tickets were sold that day?

Correct answer:

a =  93

Step-by-step explanation:

$$\begin{gathered} a+b=159 \\ 5.40\cdot a+9.70\cdot b=1142.40 \\ a+b=159 \\ 5.4a+9.7b=1142.4 \\ Pivot:Row1\leftrightarrow Row2 \\ 5.4a+9.7b=1142.4 \\ a+b=159 \\ Row2-\frac{1}{5.4}\cdot Row1\to Row2 \\ 5.4a+9.7b=1142.4 \\ -0.8b=-52.56 \\ b=\frac{-52.55555556}{-0.7962963}=66 \\ a=\frac{1142.4-9.7b}{5.4}=\frac{1142.4-9.7\cdot 66}{5.4}=93 \\ a=93 \\ b=66 \end{gathered}$$

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