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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

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

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Solve proportions: word problems

Full solution

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

Set up proportion: Understand the problem and set up a proportion. $\newline$ We know: $\newline$ ● Time taken for a $1\frac{3}{4}$ -inch candle to burn down: $7$ hours $\newline$ ● Time taken for a $1$ -inch candle to burn down: $x$ hours $\newline$ Set up a proportion that represents the problem. $\newline$ $\frac{7 \text{ hours}}{1\frac{3}{4} \text{ inches}} = \frac{x \text{ hours}}{1 \text{ inch}}$
Convert to improper fraction: Convert the mixed number to an improper fraction to simplify calculations. $\newline$ $1\frac{3}{4}$ inches is the same as $\left(1 \times 4 + 3\right)/4$ inches, which equals $\frac{7}{4}$ inches. $\newline$ Now the proportion is: $\newline$ $\frac{7 \text{ hours}}{\frac{7}{4} \text{ inches}} = \frac{x \text{ hours}}{1 \text{ inch}}$
Cross-multiply for relationship: Cross-multiply to find the relationship between the hours and inches. $\newline$ $7$ hours $*$ $1$ inch = $(7/4$ inches) $*$ $x$ hours $\newline$ This gives us: $\newline$ $7 = (7/4) * x$
Solve for x: Solve for x by multiplying both sides of the equation by the reciprocal of $\frac{7}{4}$ . $7 \times \left(\frac{4}{7}\right) = x \times \left(\frac{7}{4}\right) \times \left(\frac{4}{7}\right)$ This simplifies to: $4 = x$

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