Discount sale

At Christmas Sale after a 20% discount, the cosmetic package was priced for 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount?

Correct result:

p =  45.7143 %

Solution:

$$\begin{gathered} a-0.20a=5.60 \\ a-0.20\cdot a=5.60 \\ 0.8a=5.6 \\ a=7 \\ b=3.80\text{ eur } \\ p=100\cdot {\displaystyle \frac{a-b}{a}}=100\cdot {\displaystyle \frac{7-3.8}{7}}={\displaystyle \frac{320}{7}}=45{\displaystyle \frac{5}{7}}=45.7143\mathrm{\%} \end{gathered}$$

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