To convert the scale from 1 box = 3 inches to 1 box = 6 inches, we need to determine how the lengths in boxes will change.
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First, calculate the actual length in inches of the bureau drawer using the original scale: \[ \text{Length in inches} = \text{Length in boxes} \times \text{Scale in inches per box} = 8 , \text{boxes} \times 3 , \text{inches/box} = 24 , \text{inches} \]
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Now, using the new scale of 1 box = 6 inches, we need to find out how many boxes correspond to the same actual length of 24 inches: \[ \text{Length in boxes} = \frac{\text{Length in inches}}{\text{Scale in inches per box}} = \frac{24 , \text{inches}}{6 , \text{inches/box}} = 4 , \text{boxes} \]
Thus, the length in boxes of the new scale drawing will be 4 boxes.