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A 4(1)/(2)-inch candle burns down in 9 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 3 -inch candle to burn down?

A 412 4 \frac{1}{2} -inch candle burns down in 99 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 33 -inch candle to burn down?

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Q. A 412 4 \frac{1}{2} -inch candle burns down in 99 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 33 -inch candle to burn down?
  1. Set Proportion: We know:\newline● Time taken for a 4.54.5-inch candle to burn down: 99 hours\newline● Time taken for a 33-inch candle to burn down: xx hours\newlineChoose a proportion that represents the problem.\newline9 hours4.5 inches=x hours3 inches\frac{9 \text{ hours}}{4.5 \text{ inches}} = \frac{x \text{ hours}}{3 \text{ inches}}
  2. Cross-Multiply: We have: 94.5=x3\frac{9}{4.5} = \frac{x}{3}\newlineSelect the equation rewritten after cross-multiplying.\newlineThe two cross products:\newline9×39 \times 3 and 4.5×x4.5 \times x\newlineSo the equation becomes 9×3=4.5×x9 \times 3 = 4.5 \times x
  3. Simplify Equation: We have: 9×3=4.5×x9 \times 3 = 4.5 \times x\newlineSelect the equation we get after simplifying both sides.\newline9×3=4.5×x9 \times 3 = 4.5 \times x\newline27=4.5x27 = 4.5x
  4. Solve for x: 27=4.5x27 = 4.5x\newlineSolve for x.\newline27=4.5x27 = 4.5x \newline274.5=(4.5x)4.5\frac{27}{4.5} = \frac{(4.5x)}{4.5}\newline6=x6 = x\newlineIt would take 66 hours for a 33-inch candle to burn down.

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