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! For additional educational resources
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 \(-2\).
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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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