Two shops

In two different shops, the same skis had the same price. In the first, however, they first became more expensive by 20% and then cheaper by 5%. In the second, they were first cheaper by 5% and then more expensive by 30%, so after these adjustments in the second store, they sold them by 33.25 euros more expensive. What was the original price of these skis?

Correct answer:

x =  350 Eur

Step-by-step explanation:

$$\begin{gathered} p_1=100\%+20\%=1+\frac{20}{100}=1.2 \\ {p}_2=100\%-5\%=1-\frac{5}{100}=0.95 \\ {p}_3=100\%+30\%=1+\frac{30}{100}=1.3 \\ x\cdot p_1\cdot p_2+33.25=x\cdot p_2\cdot p_3 \\ x\cdot 1.2\cdot 0.95+33.25=x\cdot 0.95\cdot 1.3 \\ 0.095x=33.25 \\ x=\frac{33.25}{0.095}=350 \\ x=350=350\text{Eur} \end{gathered}$$

Try another example