Energy saving

They released three different independent inventions saving 15%, 17%, and 16% energy. Some considered that while the use of these inventions, the total savings will be 15% + 17% + 16% = 48%. Is this true? How much will the percent of energy save all three inventions together?

Correct answer:

p =  40.7 %

Step-by-step explanation:

$$\begin{gathered} q_1=100\%-15\%=1-\frac{15}{100}=0.85 \\ {q}_2=100\%-17\%=1-\frac{17}{100}=0.83 \\ {q}_3=100\%-16\%=1-\frac{16}{100}=0.84 \\ q=1-q_1\cdot q_2\cdot q_3=1-0.85\cdot 0.83\cdot 0.84\doteq 0.4074 \\ p=100\cdot q=100\cdot 0.4074=40.7\% \end{gathered}$$

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