To find the width of the living room on the new blueprint when using the new scale of 1 inch equals 2 feet, we can start by determining the width in feet based on the original scale and then convert it to inches in the new scale.
Step 1: Determine the original width in feet.
Using the original scale of 2 inches = 3 feet, we can find the actual width in feet. Given that the width on the original blueprint is 8 inches, we can set up the following proportion based on the original scale:
\[ \frac{2 \text{ inches}}{3 \text{ feet}} = \frac{8 \text{ inches}}{x \text{ feet}} \]
Cross-multiplying gives:
\[ 2x = 3 \times 8 \] \[ 2x = 24 \] \[ x = \frac{24}{2} = 12 \text{ feet} \]
Thus, the actual width of the living room is 12 feet.
Step 2: Convert the width in feet to the new scale.
Now, we will use the new scale of 1 inch = 2 feet to find the width on the new blueprint.
Using the new scale: \[ \frac{1 \text{ inch}}{2 \text{ feet}} = \frac{y \text{ inches}}{12 \text{ feet}} \]
Cross-multiplying gives:
\[ 1 \cdot 12 = 2y \] \[ 12 = 2y \] \[ y = \frac{12}{2} = 6 \text{ inches} \]
Thus, the width of the living room on the new blueprint is 6 inches.