The blueprint for the Moreno​'s living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inchequals6 feet. What is the width of the living room on the new​ blueprint?

Question

width equals 12 inches
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Part 1
The width on the new blueprint is
  
enter your response here inches.

Answer 1

To find the width of the living room on the new blueprint, we first need to understand the original scaling and how it translates to the new scale.

1. Original Scale:

   • The original scale is 2 inches = 3 feet.
   • This means that for every 2 inches on the blueprint, the actual dimension is 3 feet.

2. Convert the original scale to feet per inch: \[ \text{Feet per inch} = \frac{3 \text{ feet}}{2 \text{ inches}} = 1.5 \text{ feet per inch} \]

3. Determine the actual width in feet: Assuming the width of the living room is given as 12 inches on the new blueprint, we need to establish its actual width using the original scale.

   Using the conversion factor:

   • For 2 inches (from the original scale) = 3 feet, we can find out how many feet corresponds to 12 inches in the original scale: \[ \text{Feet} = \left(\frac{3}{2}\right) \times 12 = 18 \text{ feet} \]

4. Convert actual width to the new scale: The new scale is 1 inch = 6 feet. To find the width of 18 feet on the new blueprint: \[ \text{Inches} = \frac{18 \text{ feet}}{6 \text{ feet per inch}} = 3 \text{ inches} \]

Thus, the width of the living room on the new blueprint is 3 inches.