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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 $3 \frac{1}{2}$ -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 $4 \frac{1}{2}$ -inch candle to burn down? $\newline$ Answer: hours

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Solve proportions: word problems

Full solution

Q. A

3 \frac{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 \frac{1}{2}

-inch candle to burn down?

\newline

Answer: hours

Establish Relationship: Establish the relationship between the length of the candle and the time it takes to burn down. $\newline$ We know: $\newline$ ● Time taken for a $3\left(\frac{1}{2}\right)$ -inch candle to burn down: $7$ hours $\newline$ ● Time taken for a $4\left(\frac{1}{2}\right)$ -inch candle to burn down: $x$ hours $\newline$ Set up a proportion to represent the problem. $\newline$ $\frac{3.5 \text{ inches}}{7 \text{ hours}} = \frac{4.5 \text{ inches}}{x \text{ hours}}$
Set Up Proportion: Cross-multiply to find the relationship between the lengths of the candles and the time it takes to burn down. $\newline$ The two cross products are: $\newline$ $3.5 \times x$ and $7 \times 4.5$ $\newline$ So the equation becomes $3.5 \times x = 7 \times 4.5$
Cross-Multiply: Calculate the cross product on the right side of the equation. $\newline$ $7 \times 4.5 = 31.5$ $\newline$ So the equation now is $3.5 \times x = 31.5$
Calculate Cross Product: Solve for $x$ by dividing both sides of the equation by $3.5$ . $3.5 \times x = 31.5$ $x = \frac{31.5}{3.5}$ $x = 9$

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