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Elio makes candles that are
14cm tall. Each candle burns 8 hours before going out. He is wondering how many hours a
21cm tall candle can burn for.
He assumes that the relationship between the height of a candle and number of hours it burns
(h) is proportional.
How long can a
21cm tall candle burn for?
hours

Elio makes candles that are $14 \mathrm{~cm}$ tall. Each candle burns $8$ hours before going out. He is wondering how many hours a $21 \mathrm{~cm}$ tall candle can burn for. $\newline$ He assumes that the relationship between the height of a candle and number of hours it burns $(h)$ is proportional. $\newline$ How long can a $21 \mathrm{~cm}$ tall candle burn for? $\newline$ hours

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Solve proportions: word problems

Full solution

Q. Elio makes candles that are

14 \mathrm{~cm}

tall. Each candle burns

8

hours before going out. He is wondering how many hours a

21 \mathrm{~cm}

tall candle can burn for.

\newline

He assumes that the relationship between the height of a candle and number of hours it burns

(h)

is proportional.

\newline

How long can a

21 \mathrm{~cm}

tall candle burn for?

\newline

hours

Set Proportion: We know: $\newline$ ● Height of the original candle: $14\,\text{cm}$ $\newline$ ● Burn time for the original candle: $8\,\text{hours}$ $\newline$ ● Height of the new candle: $21\,\text{cm}$ $\newline$ ● Burn time for the new candle: $h\,\text{hours}$ $\newline$ Choose a proportion that represents the problem. $\newline$ $\frac{8}{14} = \frac{h}{21}$
Cross-Multiply: We have: $\frac{8}{14} = \frac{h}{21}$ $\newline$ Select the equation rewritten after cross-multiplying. $\newline$ The two cross products: $\newline$ $8 \times 21$ and $14 \times h$ $\newline$ So the equation becomes $8 \times 21 = 14 \times h$
Simplify Equation: We have: $8 \times 21 = 14 \times h$ $\newline$ Select the equation we get after simplifying both sides. $\newline$ $8 \times 21 = 14 \times h$ $\newline$ $168 = 14h$
Solve for h: $168 = 14h$ Solve for h. $168 = 14h$ $\frac{168}{14} = \frac{14h}{14}$ $12 = h$ A $21\text{cm}$ tall candle can burn for $12$ hours.

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