Question

A grid is shown with a rectangle drawn on it. The rectangle is 8 units long and 4 units wide, labeled with 8 and 4 respectively.
Scale: 1 box = 3 inches

Convert this scale drawing of a bureau drawer so that it has a scale of 1 box = 6 inches. The length in the scale drawing shown is 8 boxes. What will be the length in boxes of the new scale drawing?

(1 point)

Answer 1

To find the new length in boxes of the scale drawing when changing the scale from 1 box = 3 inches to 1 box = 6 inches, we can follow these steps:

1. **Calculate the actual dimensions in inches using the original scale**:
- The original length of the rectangle in the scale drawing is 8 boxes.
- Since each box represents 3 inches, the actual length is:
\[
\text{Actual Length} = 8 \text{ boxes} \times 3 \text{ inches/box} = 24 \text{ inches}
\]

2. **Determine the new length in boxes using the new scale**:
- Now, with 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.
- We can set up the equation:
\[
\text{New Length in boxes} \times 6 \text{ inches/box} = 24 \text{ inches}
\]
- Solving for the new length in boxes:
\[
\text{New Length in boxes} = \frac{24 \text{ inches}}{6 \text{ inches/box}} = 4 \text{ boxes}
\]

Therefore, under the new scale of 1 box = 6 inches, the length in boxes of the new scale drawing will be **4 boxes**.