Question

luke measured a swimming pool and made a scale drawing. the scale he used was 7 centimeters : 3 meters. the pool is 105 centimeters long in the drawing. how long is the actual pool?

Explanation:

Step1: Understand the scale

The scale is 7 centimeters (drawing) represents 3 meters (actual). First, convert 3 meters to centimeters: 3 meters = 300 centimeters. So the scale is 7 cm (drawing) : 300 cm (actual).

Step2: Set up the proportion

Let \( x \) be the actual length in centimeters. The drawing length is 105 cm. So we set up the proportion: \(\frac{7}{300} = \frac{105}{x}\)

Step3: Solve for \( x \)

Cross - multiply: \( 7x = 105\times300 \)
First, calculate \( 105\times300 = 31500 \)
Then, \( x=\frac{31500}{7}=4500 \) centimeters.

Step4: Convert back to meters

Since 1 meter = 100 centimeters, divide 4500 by 100: \( 4500\div100 = 45 \) meters.

Answer:

The actual length of the pool is 45 meters.