To convert the length from the original scale of 1 box = 6 inches to the new scale of 1 box = 12 inches, we first need to determine the length in inches for the original scale.
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Calculate the length in inches for the original scale: \[ \text{Original Length} = \text{Number of Boxes} \times \text{Scale Factor} \] \[ \text{Original Length} = 10 \text{ boxes} \times 6 \text{ inches/box} = 60 \text{ inches} \]
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Now, to find the length in the new scale where 1 box = 12 inches, we need to convert the original 60 inches back into boxes: \[ \text{New Length in Boxes} = \frac{\text{Original Length}}{\text{New Scale Factor}} \] \[ \text{New Length in Boxes} = \frac{60 \text{ inches}}{12 \text{ inches/box}} = 5 \text{ boxes} \]
Thus, the length of the boxes in the new drawing will be 5 boxes.