Use the image to answer the question.
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)
The length in boxes of the new scale drawing will be 4 boxes.
4 is correct
To solve this problem, we need to first understand the given scale and convert it to the new scale.
The given scale is 1 box = 3 inches. We are asked to convert it to a new scale of 1 box = 6 inches. This means that every box in the new scale will represent 6 inches instead of 3 inches.
To find the length in boxes of the new scale drawing, we need to determine how many boxes will represent the same length as the original drawing.
In the original drawing, the length is given as 8 boxes. Since each box represents 3 inches, the total length of the original drawing is 8 boxes * 3 inches/box = 24 inches.
To find the length in boxes of the new scale drawing, we can use the ratio of the new scale to the original scale. The new scale is 1 box = 6 inches, and the original scale is 1 box = 3 inches.
Using the ratio, we can set up a proportion:
1 box (new scale) / 6 inches = x boxes (original scale) / 24 inches
Cross-multiplying, we get:
6 inches * x boxes (original scale) = 1 box (new scale) * 24 inches
Simplifying, we have:
6x = 24
To solve for x, we divide both sides by 6:
x = 24 / 6 = 4
Therefore, the length in boxes of the new scale drawing will be 4 boxes.
To convert the scale from 1 box = 3 inches to 1 box = 6 inches, we need to multiply the length in the original scale drawing by a scale factor of 2.
Given that the original length is 8 boxes, we can find the length in the new scale drawing by multiplying 8 by the scale factor:
New length = 8 x 2 = 16 boxes.
Therefore, the length in boxes of the new scale drawing will be 16.