To convert the width of the living room from the original scale of 2 inches equals 3 feet to the new scale of 1 inch equals 5 feet, we need to first understand how to convert between the scales.
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Determine the width in feet on the original blueprint.
- Let's assume the width on the original blueprint is \( x \) inches.
- According to the original scale, \( 2 \) inches corresponds to \( 3 \) feet, so: \[ \text{Width in feet} = \frac{3}{2} \times x = 1.5x \text{ feet} \]
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Now we need to convert this width from feet to inches using the new scale.
- In the new scale, \( 1 \) inch corresponds to \( 5 \) feet.
- To find out how many inches represent \( 1.5x \) feet in the new scale, we can set up the relationship: \[ \text{Width in inches (new scale)} = \frac{1.5x \text{ feet}}{5 \text{ feet/inch}} = \frac{1.5x}{5} \text{ inches} \]
- This simplifies to: \[ \text{Width in inches (new scale)} = 0.3x \]
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Now, if we know that the width of the living room on the new blueprint is given as \( 10 \) inches, we can find the original width \( x \): \[ 0.3x = 10 \implies x = \frac{10}{0.3} \approx 33.33 \text{ inches} \]
Thus, the width of the living room on the original blueprint is approximately \( 33.33 \) inches. When converted to the new blueprint scale of \( 1 \) inch equals \( 5 \) feet, it equals \( 10 \) inches.
In conclusion:
- If the question is asking for the width on the new blueprint, the final answer will be:
The width on the new blueprint is \(\boxed{10}\) inches.