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A
1(3)/(4)-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 1-inch candle to burn down?
Answer: hours
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A $1 \frac{3}{4}$ -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 $1$ -inch candle to burn down? $\newline$ Answer: hours $\newline$ Submit Answer

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Solve proportions: word problems

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Q. A

1 \frac{3}{4}

-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

1

-inch candle to burn down?

\newline

Answer: hours

\newline

Submit Answer

Establish Relationship: Establish the known relationship. $\newline$ We know: $\newline$ ● A $1\frac{3}{4}$ -inch candle burns down in $7$ hours. $\newline$ ● We want to find out how long it takes for a $1$ -inch candle to burn down. $\newline$ Set up a proportion to represent the problem. $\newline$ $\left(1 + \frac{3}{4}\right) \text{ inches} / 7 \text{ hours} = 1 \text{ inch} / x \text{ hours}$
Set Up Proportion: Convert the mixed number to an improper fraction to simplify calculations. $\newline$ $1\frac{3}{4}$ inches is the same as $\frac{4}{4} + \frac{3}{4}$ inches, which equals $\frac{7}{4}$ inches. $\newline$ Now the proportion is: $\newline$ $\frac{7}{4}$ inches / $7$ hours = $1$ inch / $x$ hours
Convert Mixed Number: Cross-multiply to find the relationship between the lengths and times. $\newline$ $(\frac{7}{4}) \times x = 7 \times 1$ $\newline$ $\frac{7x}{4} = 7$
Cross-Multiply: Solve for $x$ by multiplying both sides of the equation by $\frac{4}{7}$ . $\left(\frac{7x}{4}\right) \cdot \left(\frac{4}{7}\right) = 7 \cdot \left(\frac{4}{7}\right)$ $x = 4$

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