Lenka and money

When Lenka bought pants from 1/3 of her savings and a shirt from 1/5 and 1/8 spent at the hairdresser, she was left with 328 CZK.

How much money was saved? How much do hairdressers cost?

Correct answer:

x =  960
k =  120

Step-by-step explanation:

$$\begin{gathered} x-\frac{1}{3}x-\frac{1}{5}x-k=328 \\ k=\frac{1}{8}x \\ x-1/3\cdot x-1/5\cdot x-k=328 \\ k=1/8\cdot x \\ 15k-7x=-4920 \\ 8k-x=0 \\ Row2-\frac{8}{15}\cdot Row1\to Row2 \\ 15k-7x=-4920 \\ 2.73x=2624 \\ x=\frac{2624}{2.73333333}=960 \\ k=\frac{-4920+7x}{15}=\frac{-4920+7\cdot 960}{15}=120 \\ k=120 \\ x=960 \end{gathered}$$

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