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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 4(1)/(2)-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 412 4 \frac{1}{2} -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 412 4 \frac{1}{2} -inch candle to burn down?\newlineAnswer: hours
  1. Establish Relationship: Establish the relationship between the length of the candle and the time it takes to burn down.\newlineWe know:\newline● Time taken for a 3(12)3\left(\frac{1}{2}\right)-inch candle to burn down: 77 hours\newline● Time taken for a 4(12)4\left(\frac{1}{2}\right)-inch candle to burn down: xx hours\newlineSet up a proportion to represent the problem.\newline3.5 inches7 hours=4.5 inchesx hours\frac{3.5 \text{ inches}}{7 \text{ hours}} = \frac{4.5 \text{ inches}}{x \text{ hours}}
  2. Set Up Proportion: Cross-multiply to find the relationship between the lengths of the candles and the time it takes to burn down.\newlineThe two cross products are:\newline3.5×x3.5 \times x and 7×4.57 \times 4.5\newlineSo the equation becomes 3.5×x=7×4.53.5 \times x = 7 \times 4.5
  3. Cross-Multiply: Calculate the cross product on the right side of the equation.\newline7×4.5=31.57 \times 4.5 = 31.5\newlineSo the equation now is 3.5×x=31.53.5 \times x = 31.5
  4. Calculate Cross Product: Solve for xx by dividing both sides of the equation by 3.53.5.3.5×x=31.53.5 \times x = 31.5x=31.53.5x = \frac{31.5}{3.5}x=9x = 9

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