To find the actual length of the countertop based on the scale drawing, we first need to understand the scale Gwen used, which is 11 inches in the drawing to 5 feet in reality.
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Convert 5 feet to inches: Since there are 12 inches in a foot, we calculate: \[ 5 \text{ feet} \times 12 \text{ inches/foot} = 60 \text{ inches} \]
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Set up the scale ratio: The scale is 11 inches (drawing) : 60 inches (actual). This can be expressed as: \[ \frac{11 \text{ inches}}{60 \text{ inches}} = \frac{22 \text{ inches (drawing)}}{x \text{ inches (actual)}} \]
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Cross-multiply to find x: \[ 11 \cdot x = 60 \cdot 22 \]
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Calculate \(60 \cdot 22\): \[ 60 \cdot 22 = 1320 \]
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Now we have: \[ 11x = 1320 \]
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Solve for \(x\): \[ x = \frac{1320}{11} = 120 \]
So, the actual length of the countertop is 120 inches.
To convert this back to feet for clarity: \[ \frac{120 \text{ inches}}{12 \text{ inches/foot}} = 10 \text{ feet} \]
Thus, the actual length of the countertop is 120 inches or 10 feet.