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Jenna measured a swimming pool and made a scale drawing. The pool is $20\,\text{centimeters}$ long in the drawing. The actual pool is $40\,\text{meters}$ long. What scale did Jenna use for the drawing? $\newline$ $1\,\text{centimeter} : \_\_\_\_\,\text{meters}$

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Scale drawings: word problems

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Q. Jenna measured a swimming pool and made a scale drawing. The pool is

20\,\text{centimeters}

long in the drawing. The actual pool is

40\,\text{meters}

long. What scale did Jenna use for the drawing?

\newline

1\,\text{centimeter} : \_\_\_\_\,\text{meters}

Identify Measurements: Identify the given measurements. $\newline$ Jenna's scale drawing length of the pool = $20$ centimeters $\newline$ Actual length of the pool = $40$ meters $\newline$ We need to find the scale in the form of $1$ centimeter : $\_\_$ meters.
Set Up Ratio: Set up the ratio of the drawing length to the actual length. $\newline$ Ratio = $(\text{Drawing length}) / (\text{Actual length})$ $\newline$ Ratio = $(20 \text{ centimeters}) / (40 \text{ meters})$ $\newline$ Since $1 \text{ meter} = 100 \text{ centimeters}$ , we need to convert meters to centimeters to have the same units. $\newline$ Ratio = $(20 \text{ centimeters}) / (40 \text{ meters} \times 100 \text{ centimeters/meter})$
Perform Calculation: Perform the calculation to find the scale. $\text{Ratio} = \frac{20 \text{ centimeters}}{4000 \text{ centimeters}}$ Now, simplify the ratio by dividing both the numerator and the denominator by $20$ . $\text{Ratio} = \frac{20/20 \text{ centimeters}}{4000/20 \text{ centimeters}}$ $\text{Ratio} = 1 \text{ centimeter} / 200 \text{ centimeters}$ Since we want the scale in terms of meters, we convert $200 \text{ centimeters}$ back to meters. $\text{Ratio} = 1 \text{ centimeter} / (200 \text{ centimeters} \times 1 \text{ meter}/100 \text{ centimeters})$
Simplify Ratio: Simplify the ratio to find the scale. $\newline$ Ratio = $1$ centimeter / $2$ meters $\newline$ So, the scale Jenna used for the drawing is $1$ centimeter : $2$ meters.

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