Organizers 2

The organizers of a concert sold tickets for a total of 18,000 CZK. The seats in the auditorium are divided into two differently priced sections. A ticket in section 1 costs 500 CZK. A total of 300 people attended the concert, with 60 fewer people in section 1 than in section 2. How many tickets were sold for section 1? How many people does section 2 hold?

Final Answer:

b =  180

Step-by-step explanation:

$$\begin{gathered} a+b=300 \\ a=b-60 \\ a+b=300 \\ a-b=-60 \\ Row2-Row1\to Row2 \\ -2b=-360 \\ b=\frac{-360}{-2}=180 \\ a=300-b=300-180=120 \\ a=120 \\ b=180 \\ \text{ Verifying Solution: } \\ 18000=500\cdot a+c\cdot b \\ 18000=500\cdot 120+c\cdot 180 \\ 180c=-42000 \\ c=\frac{-42000}{180}=-233.33333333 \\ c=\frac{-700}{3}\doteq -233.333333 \end{gathered}$$

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