Camp cost distribution

The department consists of 80 children and adults. The camp cost them a total of 116,400 CZK. Each child paid 1200 CZK and each adult 1800 CZK. How many adult participants were there, how much did the children pay for the camp, and who paid more money for the camp, and by how much?

Final Answer:

a =  34
x =  55200 Kc

Step-by-step explanation:

$$\begin{gathered} a+b=80 \\ 1800a+1200b=116400 \\ 1800\cdot a+1200\cdot b=116400 \\ a+b=80 \\ 1800a+1200b=116400 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{1800}\cdot Row1\to Row2 \\ 0.33b=15.33 \\ b=\frac{15.33333333}{0.33333333}=46 \\ a=\frac{116400-1200b}{1800}=\frac{116400-1200\cdot 46}{1800}=34 \\ a=34 \\ b=46 \end{gathered}$$

$$\begin{gathered} x=1200\cdot b=1200\cdot 46=55200=55200\text{Kc} \\ y=1800\cdot a=1800\cdot 34=61200\text{Kc} \\ x<y \end{gathered}$$

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