Correspond 81207

Zuzana, Anna, and Eliška receive pocket money every month. They donated part - Zuzana 40%, Anna 50% and Eliška CZK 195. If we add up all 3 amounts and divide the sum by 3, the result will correspond to 4/9 of the pocket money of each of the girls. What is each of them's pocket money?

Correct answer:

x =  450

Step-by-step explanation:

$$\begin{gathered} p_1=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {p}_2=50\%=\frac{50}{100}=\frac{1}{2}=0.5 \\ (p_1\cdot x+p_2\cdot x+195)/3=\frac{4}{9}\cdot x \\ (0.4\cdot x+0.5\cdot x+195)/3=\frac{4}{9}\cdot x \\ (0.4\cdot x+0.5\cdot x+195)/3=4/9\cdot x \\ 1.3x=585 \\ x=\frac{585}{1.3}=450 \\ x=450 \end{gathered}$$

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