Ratios and Scale Drawings

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📐 Part 1: Understanding Ratios and Scale

1. A map has a scale of 1 inch = 50 miles. If two cities are 3 inches apart on the map, what is the actual distance between them?

150 miles

53 miles

17 miles

100 miles

2. Which of the following are equivalent ratios to 2:6? (Check all that apply)

1:3

4:12

3:9

6:2

3. A blueprint uses a scale of 1/4 inch = 1 foot. If a room measures 2 inches on the blueprint, how long is the actual room?

2 feet

4 feet

8 feet

6 feet

4. The ratio of boys to girls in a class is 3:5. If there are 15 girls, how many boys are there?

✏️ Part 2: Multi-Step Problem Solving

5. A recipe calls for 2 cups of flour for every 3 cups of sugar. If you want to make a larger batch using 9 cups of sugar, how many cups of flour will you need? Show your work.

6. On a scale drawing, a car is 2.5 inches long. The scale is 1 inch = 4 feet. What is the actual length of the car in feet?

Set up your proportion: _______ = _______

Actual length: __________ feet

7. A model airplane is built using a scale of 1:48. If the model's wingspan is 10 inches, what is the wingspan of the real airplane in feet? (Hint: Convert inches to feet in your final answer)

🎯 Part 3: Real-World Applications

8. You are designing a scale drawing of your bedroom. The actual room is 12 feet by 10 feet. If you use a scale of 1 inch = 2 feet, what will be the dimensions of your drawing?

Drawing length: __________ inches

Drawing width: __________ inches

9. Explain in your own words: What is the difference between a ratio and a proportion? Give an example of each.

10. Challenge Problem: A photograph is enlarged so that a 4-inch by 6-inch photo becomes an 8-inch by 12-inch photo. What scale factor was used for the enlargement? If you wanted to make an even larger version that is 16 inches long, how wide would it be?