To find the scale that Luna used for her drawing, we can set up a proportion to compare the real-life dimensions to the dimensions in the scale drawing.
The real length of the schoolyard is 175 meters, and in the drawing, it is 25 centimeters.
First, we need to convert the real-life measurement to centimeters since the scale drawing is in centimeters: 1 meter = 100 centimeters, so: 175 meters = 175 × 100 = 17,500 centimeters.
Now we can set up the scale: \[ \text{Scale} = \frac{\text{Length in drawing}}{\text{Real length}} = \frac{25 \text{ cm}}{17500 \text{ cm}}. \]
To express the scale in the format of "1 centimeter : x meters", we can find out how many real meters correspond to 1 centimeter in the drawing.
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First, compute the scale factor: \[ \frac{25 \text{ cm}}{17500 \text{ cm}} = \frac{1}{700}. \]
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This tells us that 1 centimeter in the drawing represents 700 centimeters in reality.
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To convert 700 centimeters back to meters: \[ 700 \text{ cm} = \frac{700}{100} \text{ m} = 7 \text{ m}. \]
Thus, the scale that Luna used for the drawing is: \[ 1 \text{ cm} : 7 \text{ m}. \]