The image you've uploaded shows a homework question about ratios and proportions, where you're tasked with finding the actual dimensions of a room, given the scale of the floor plan.

To clarify:

• The scale of the drawing is 1:76 (meaning 1 inch on the drawing represents 76 inches in real life).
• The room's dimensions on the drawing are 7 7/8 inches by 3 1/4 inches.
• You are asked to find the actual dimensions in feet.

To solve the problem:

1. Convert the drawing dimensions to the actual size using the scale.

   • Length: $\text{Actual length} = \text{Drawing length} \times \text{Scale} = \left(7 + \frac{7}{8}\right) \times 76 \text{ inches}$
   • Width: $\text{Actual width} = \text{Drawing width} \times \text{Scale} = \left(3 + \frac{1}{4}\right) \times 76 \text{ inches}$

2. Convert inches to feet (since 12 inches = 1 foot):

   • For the length and width, divide the resulting inches by 12 to get the dimensions in feet.

Let's calculate these values now.

I'll proceed with the math to find the actual dimensions for you. Given values scale = 76 # Scale is 1:76 drawing_length = 7 + 7/8 # 7 7/8 inches drawing_width = 3 + 1/4 # 3 1/4 inches

Convert to actual dimensions in inches

actual_length_inches = drawing_length * scale actual_width_inches = drawing_width * scale

Convert to feet (12 inches = 1 foot)

actual_length_feet = actual_length_inches / 12 actual_width_feet = actual_width_inches / 12

actual_length_feet, actual_width_feetThe actual dimensions of the room are approximately:

• Length: 49.88 feet
• Width: 20.58 feet

Would you like further explanations on any part of the solution or additional help?

Here are 5 related questions to explore further:

1. How can I convert other types of measurements like centimeters or meters using ratios?
2. What are some real-life examples of using scale drawings in architecture?
3. How can I verify the accuracy of my scale calculations?
4. What is the importance of precision when calculating areas based on scale drawings?
5. How do I handle scale conversions if the drawing uses a different unit (e.g., centimeters)?

Tip: Always double-check the units you are working with, especially when converting between them!