Use the image to answer the 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)
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page 16 of 17
To convert the scale drawing of the bureau drawer to a scale of 1 box = 6 inches, we need to adjust the scale factor. The original scale is 1 box = 3 inches, and we want to double the length of the scale drawing.
To find the new length in boxes, we can set up a ratio:
$\frac{\text{new length in boxes}}{\text{original length in boxes}} = \frac{\text{new scale}}{\text{original scale}}$
Let's substitute the given information into the equation:
$\frac{\text{new length in boxes}}{8} = \frac{6}{3}$
Simplifying the ratio:
$\frac{\text{new length in boxes}}{8} = 2$
Now we can solve for the new length in boxes by multiplying both sides of the equation by 8:
$\text{new length in boxes} = 8 \times 2 = 16$
The length in boxes of the new scale drawing will be 16.