Math Problem Statement
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Solution
Let's break down the math problems from the image you've uploaded. The problems deal with using scales to find distances. I'll interpret the equations and provide detailed solutions.
Problem 1:
Given: Tasha makes a scale drawing of points of interest between two parks. The drawing uses a scale of 2 cm = 6 meters.
In her drawing:
- The distance between the parks is 12 cm.
To find: The actual distance between the parks.
Solution: The scale is . Therefore: Cross-multiply: Solve for : Answer: The actual distance is 36 meters.
Problem 2:
Given: Robert is building a scale model of a shelf. The actual shelf is 6 feet tall, and his model will be of the actual size.
To find:
- The height of the model.
- Whether it fits in a space that is 6 inches tall.
Solution: First, convert the actual height of the shelf to inches: Now, use the scale : Since the model is 6 inches tall, it will not fit in a space that is also 6 inches tall, as there would be no clearance.
Answer: The model height is 6 inches, and it will not fit in the 6-inch tall space.
Problem 3:
Given: Amber is making a scale drawing of a movie screen. The actual dimensions of the screen are 20 feet tall and 60 feet wide. The width of the screen in the drawing is 9 cm.
To find: The height of the screen in the drawing.
Solution: We have the following proportions based on the actual width and height: Cross-multiply: Solve for : Answer: The height of the screen in the drawing is 3 cm.
Summary of Answers:
- The actual distance between the parks is 36 meters.
- The model height is 6 inches, and it will not fit in the space.
- The height of the screen in the drawing is 3 cm.
Would you like any further details or explanations?
Here are 5 related questions to expand your knowledge:
- How would the result change in problem 1 if the drawing distance were 15 cm?
- If Robert wanted his shelf model to fit, what would the scale factor need to be?
- How can you convert different units (e.g., feet to meters) when using scales?
- What happens if Amber increases the width of her drawing? How would that affect the height?
- Can you solve similar problems involving different scale ratios?
Tip:
When solving scale problems, always keep the units consistent (e.g., convert feet to inches or vice versa) before applying the proportion to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Proportions
Scale Drawing
Unit Conversion
Formulas
Cross-multiplication: (a/b) = (c/d)
Proportion scaling: drawing_length / drawing_scale = actual_length / actual_scale
Theorems
Proportion Theorem
Suitable Grade Level
Grades 5-7
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