Scale and Proportions in Word Problems

The video tutorial covers various mathematical concepts for 7th-grade students, including scale drawings, calculating scales for drawings, identifying equivalent scales, determining the area of scaled triangles, calculating costs of items based on unit price, and completing a recipe table for soap solution batches. Each section provides practical examples and step-by-step explanations to help students understand and apply these concepts effectively.

What is the most appropriate scale for drawing the Empire State Building on an 8.5 by 11 inch paper?

• 1 cm to 10 m

• 1 cm to 200 m

• 1 cm to 50 m

• 1 cm to 100 m

If a scale drawing of a house has an area of 25 square inches and the actual house is 25 square feet, what is the scale of the drawing?

• 1 inch to 5 feet

• 1 inch to 9 feet

• 1 inch to 12 feet

• 1 inch to 15 feet

Which of these scales is equivalent to 3 cm to 4 km?

• 2 cm to 5 km

• 1.5 cm to 3 km

• 1 cm to 2 km

• 0.75 cm to 1 km

If the smaller triangle has an area of 9 square units, what is the area of the larger triangle if its sides are twice as long?

• 27 square units

• 18 square units

• 45 square units

• 36 square units

How much would 10 bottles of water cost if each bottle is priced at $1.25?

• $17.50

• $10.00

• $12.50

• $15.00

What is the cost of 20 bottles of water at $1.25 each?

• $22.50

• $25.00

• $20.00

• $27.50

How much would 50 bottles of water cost at the rate of $1.25 per bottle?

• $60.00

• $62.50

• $55.00

• $50.00

If one batch of soap solution requires 6 cups of water, how many cups are needed for 4 batches?

• 12 cups

• 18 cups

• 24 cups

• 30 cups

For 8 batches of soap solution, how many cups of detergent are required if one batch needs 1 cup?

• 4 cups

• 10 cups

• 6 cups

• 8 cups

If 2 batches of soap solution require 12 cups of water, how many cups are needed for 3 batches?

• 24 cups

• 18 cups

• 20 cups

• 22 cups