Question
Antonio measured a house and its lot and made a scale drawing. The scale of the drawing was 5 centimeters = 7 meters. What is the drawing's scale factor?
Simplify your answer and write it as a ratio, using a colon.
Simplify your answer and write it as a ratio, using a colon.
Answers
GPT-4o mini
To find the drawing's scale factor in terms of a ratio, we use the information provided: the scale drawing of the house represents 5 centimeters for every 7 meters in reality.
First, we need to express both measurements in the same units. Let's convert 7 meters to centimeters, since 1 meter = 100 centimeters:
\[
7 \text{ meters} = 7 \times 100 = 700 \text{ centimeters}
\]
Now we can set up the ratio of the drawing to the actual size:
\[
\text{Drawing} : \text{Actual size} = 5 \text{ cm} : 700 \text{ cm}
\]
To simplify the ratio, we divide both sides of the ratio by 5:
\[
5 \div 5 : 700 \div 5 = 1 : 140
\]
Thus, the drawing's scale factor, simplified as a ratio, is:
\[
\boxed{1:140}
\]
First, we need to express both measurements in the same units. Let's convert 7 meters to centimeters, since 1 meter = 100 centimeters:
\[
7 \text{ meters} = 7 \times 100 = 700 \text{ centimeters}
\]
Now we can set up the ratio of the drawing to the actual size:
\[
\text{Drawing} : \text{Actual size} = 5 \text{ cm} : 700 \text{ cm}
\]
To simplify the ratio, we divide both sides of the ratio by 5:
\[
5 \div 5 : 700 \div 5 = 1 : 140
\]
Thus, the drawing's scale factor, simplified as a ratio, is:
\[
\boxed{1:140}
\]