Energy saving

They were released three different, independent inventions saving 20%, 24% and 15% energy. Some considered that while the use of these inventions, the total savings will be 20% + 24% + 15% = 59%. Is this true? How much percent of energy will save all three inventions together?

Correct answer:

p =  48.32 %

Step-by-step explanation:

$$\begin{gathered} q_1=20\mathrm{\%}=1-{\displaystyle \frac{20}{100}}=0.8 \\ {q}_2=24\mathrm{\%}=1-{\displaystyle \frac{24}{100}}=0.76 \\ {q}_3=15\mathrm{\%}=1-{\displaystyle \frac{15}{100}}=0.85 \\ q=1-q_1\cdot q_2\cdot q_3=1-0.8\cdot 0.76\cdot 0.85={\displaystyle \frac{302}{625}}=0.4832 \\ p=100\cdot q=100\cdot 0.4832={\displaystyle \frac{1208}{25}}={\displaystyle \frac{1208}{25}}\mathrm{\%}=48.32\mathrm{\%} \end{gathered}$$

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