Theater ticket viewers

Although the price of a theater ticket rose by 20 percent, sales rose by only 8 percent. By what percentage did the number of viewers have to drop?

Final Answer:

p₃ =  10 %

Step-by-step explanation:

$$\begin{gathered} p_1=100\%+20\%=1+\frac{20}{100}=1.2 \\ {p}_2=100\%+8\%=1+\frac{8}{100}=1.08 \\ {p}_1\cdot r=p_2 \\ r=p_2/p_1=1.08/1.2=\frac{9}{10}=0.9 \\ r=1-p_3/100 \\ {p}_3=100\cdot (1-r)=100\cdot (1-0.9)=10\% \end{gathered}$$

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