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A 3(1)/(2)-inch candle burns down in 7 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 5 -inch candle to burn down? Answer: hours

A 312 3 \frac{1}{2} -inch candle burns down in 77 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 55 -inch candle to burn down?\newlineAnswer: hours

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Q. A 312 3 \frac{1}{2} -inch candle burns down in 77 hours. Assuming the candles are the same thickness and make (that is, directly proportional), how long would it take a 55 -inch candle to burn down?\newlineAnswer: hours
  1. Set Proportion: We know:\newline● Time taken for a 3.53.5-inch candle to burn down: 77 hours\newline● Time taken for a 55-inch candle to burn down: xx hours\newlineChoose a proportion that represents the problem.\newline73.5=x5\frac{7}{3.5} = \frac{x}{5}
  2. Cross-Multiply: We have: 73.5=x5\frac{7}{3.5} = \frac{x}{5}\newlineSelect the equation rewritten after cross-multiplying.\newlineThe two cross products:\newline7×57 \times 5 and 3.5×x3.5 \times x\newlineSo the equation becomes 7×5=3.5×x7 \times 5 = 3.5 \times x
  3. Simplify Equation: We have: 7×5=3.5×x7 \times 5 = 3.5 \times x\newlineSelect the equation we get after simplifying both sides.\newline7×5=3.5×x7 \times 5 = 3.5 \times x\newline35=3.5x35 = 3.5x
  4. Solve for x: 35=3.5x35 = 3.5x\newlineSolve for x.\newline35=3.5x35 = 3.5x\newline353.5=3.5x3.5\frac{35}{3.5} = \frac{3.5x}{3.5}\newline10=x10 = x\newlineIt would take 1010 hours for a 55-inch candle to burn down.

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