Question

scale drawings and maps
solve, using a proportion.

1. if 4 inches represents 100 miles on a scale drawing, how long would a line segment be that represents 50 miles?

1. on a map drawn to scale, 7 cm represents 280 km. how many kilometers are represented by a line 8 centimeters long?

1. on a scale drawing, 4 inches represents 25 miles. if a line segment on the drawing is 6 inches long, what distance does this line segment represent?

1. on a map drawn to scale, 2 cm represents 870 km. how long would a line segment be that represents 130 kilometers?

1. if 3 inches represents 90 miles on a scale drawing, how long would a line segment be that represents 240 miles?

ratios & proportions – review packet – exercises hanlonmath.com 5

Explanation:

Problem 1

Step1: Define the proportion

Let \( x \) be the length in inches. The proportion is \( \frac{4}{100}=\frac{x}{50} \)

Step2: Solve for \( x \)

Cross - multiply: \( 100x = 4\times50 \)
\( 100x=200 \)
Divide both sides by 100: \( x=\frac{200}{100}=2 \)

Step1: Define the proportion

Let \( x \) be the distance in km. The proportion is \( \frac{7}{280}=\frac{8}{x} \)

Step2: Solve for \( x \)

Cross - multiply: \( 7x = 280\times8 \)
\( 7x = 2240 \)
Divide both sides by 7: \( x=\frac{2240}{7}=320 \)

Step1: Define the proportion

Let \( x \) be the distance in miles. The proportion is \( \frac{4}{25}=\frac{6}{x} \)

Step2: Solve for \( x \)

Cross - multiply: \( 4x=25\times6 \)
\( 4x = 150 \)
Divide both sides by 4: \( x=\frac{150}{4}=37.5 \)

Answer:

2 inches

Problem 2