Ratio, Proportion and Percentages Puzzle -Critical Thinking 8

This kind of math puzzles is an educational activity for practicing children's math skills. It's also helpful for adults to have fun and challenge their brains!

Ratio, Proportion and Percentages Puzzle -Critical Thinking 8

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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Math and Critical Thinking Challenges: For the Middle and High School Student