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A grid is shown with a rectangle drawn on it. The rectangle is 7 units long and 3 units wide, labeled with 7 and 3 respectively.

Scale: 1 box = 4 inches

Ana Maria needs to convert this scale drawing from a scale of 1 box = 4 inches to a scale of 1 box = 2 inches. The width in the scale drawing shown is 3 boxes. What will be the width in boxes of the new drawing?

(1 point)
Responses

14
14

9
9

1.5
1.5

6
6
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1 answer

To find the width in boxes of the new drawing after changing the scale, we can follow these steps:

  1. Determine the current dimensions in inches:

    • The current width in the scale drawing is 3 boxes. With the scale of 1 box = 4 inches, the actual width in inches is: \[ 3 \text{ boxes} \times 4 \text{ inches/box} = 12 \text{ inches} \]

  2. Convert to the new scale:

    • We need to express the width in terms of the new scale, which is 1 box = 2 inches.
    • To find the new width in boxes, we take the actual width in inches and divide it by the number of inches per box in the new scale: \[ \text{New width in boxes} = \frac{12 \text{ inches}}{2 \text{ inches/box}} = 6 \text{ boxes} \]

Therefore, the width in boxes of the new drawing will be 6.