Camera double discount

The camera was reduced twice, first by one-fifth of the original price and then by a quarter of its new price. After the second discount, the camera cost CZK 8,100. How much did he face before the discounts?

Final Answer:

x =  13500

Step-by-step explanation:

$$\begin{gathered} q_1=1-\frac{1}{5}=\frac{1\cdot 5}{5}-\frac{1}{5}=\frac{5}{5}-\frac{1}{5}=\frac{5-1}{5}=\frac{4}{5}=0.8 \\ {q}_2=1-\frac{1}{4}=\frac{1\cdot 4}{4}-\frac{1}{4}=\frac{4}{4}-\frac{1}{4}=\frac{4-1}{4}=\frac{3}{4}=0.75 \\ x\cdot q_1\cdot q_2=8100 \\ x=\frac{8100}{q_1\cdot q_2}=\frac{8100}{\frac{4}{5}\cdot \frac{3}{4}}=13500 \end{gathered}$$

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