How to Do Ratio, Proportion, and Percentages Puzzle -Critical Thinking 8
This kind of math puzzle is an educational activity for practicing children's math skills. It's also helpful for adults to have fun and challenge their brains!
Challenge:
If \(5^x + 5^{x+1} + 5^{x+2}=\frac{31}{25}\), what is the value of x?
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The correct answer is \(-2\).
Solve for x:
\(5^x + 5^{x+1} + 5^{x+2}=\frac{31}{25}\)
The common factor is \(5^x\). Then,
\(5^x(1+5^1+5^2)=\frac{31}{25}⇒5^x(31)=\frac{31}{25}⇒5^x=\frac{\frac{31}{25}}{31}⇒\)
\(5^x=\frac{31}{25}÷\frac{31}{1}=\frac{31}{25}×\frac{1}{31}=\frac{1}{25}\)
\(\frac{1}{25}=5^{-2}\) Then: \(5^x=5^{-2}⇒ x = -2\)
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