The price

The calculator's price gradually decreased from 65 euros to 30 euros, then to 10 euros, and finally to 4 euros. What percentage were the individual reductions? What percentage of the original price was reduced?

Correct answer:

p₁ =  53.8462 %
p₂ =  66.6667 %
p₃ =  60 %
p₄ =  93.8462 %

Step-by-step explanation:

$$\begin{gathered} c_1=65\text{Eur} \\ {c}_2=30\text{Eur} \\ {c}_3=10\text{Eur} \\ {c}_4=4\text{Eur} \\ {p}_1=100\cdot \frac{c_1-c_2}{c_1}=100\cdot \frac{65-30}{65}=\frac{700}{13}\%=53.8462\% \end{gathered}$$

$p_2=100\cdot \frac{c_2-c_3}{c_2}=100\cdot \frac{30-10}{30}=\frac{200}{3}\%=66.6667\%$

$p_3=100\cdot \frac{c_3-c_4}{c_3}=100\cdot \frac{10-4}{10}=60\%$

$$\begin{gathered} p_4=100\cdot \frac{c_1-c_4}{c_1}=100\cdot \frac{65-4}{65}=\frac{1220}{13}\doteq 93.8462\% \\ \text{ Verifying Solution: } \\ p=p_1+p_2+p_3=\frac{700}{13}+\frac{200}{3}+60=\frac{7040}{39}\doteq 180.5128\% \\ p\ne p_4 \end{gathered}$$

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