To find the width of the living room on the new blueprint, we first need to determine the width in feet from the original blueprint and then convert it to the new scale.
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Original Scale: 2 inches = 3 feet
- This means that for every 2 inches on the original blueprint, the real-life width is 3 feet.
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Calculate the width in feet for the original scale:
- Let’s assume the width on the original blueprint is \( W \) inches.
- From the ratio, we can say: \[ \text{Width in feet} = \left( \frac{3 \text{ feet}}{2 \text{ inches}} \right) \times W \]
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New Scale: 1 inch = 4 feet
- For the new blueprint, we can determine the width using the new scale. The width in feet will be: \[ \text{Width in feet} = 4 \text{ feet} \times \text{Width on new blueprint in inches} \]
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Setting the widths equal:
- Since both represent the same real-life width in feet, we can set them equal to one another: \[ \left( \frac{3}{2} \times W \right) = (4 \times \text{New Width}) \]
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Solving for the new width:
- Rearranging the equation to solve for the new width: \[ \text{New Width} = \left( \frac{3}{2} \times W \right) \div 4 \] \[ \text{New Width} = \frac{3W}{8} \]
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Now, let's plug in the original width. If we are provided that the original width equals 8 inches: \[ \text{New Width} = \frac{3 \times 8}{8} = 3 \text{ inches} \]
Therefore, the width on the new blueprint is 3 inches.
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