Use the image to answer the question.
8
4
Scale: 1 box = 3 inches
Convert this scale drawing of a bureau drawer so that it has a scale of 1box = 6 inches. The length in the scale drawing shown is 8 boxes. What will be the length in boxes of the new scale drawing?
To solve this problem, we need to use the concept of ratio and proportion.
Given:
Scale of the current drawing: 1 box = 3 inches
Length in the current drawing: 8 boxes
We want to convert to a new scale:
Scale of the new drawing: 1 box = 6 inches
To find the length in boxes of the new scale drawing, we need to find the ratio between the two scales and then multiply it by the length in the current drawing.
First, let's find the ratio between the two scales:
Ratio = (Length in the new scale drawing) / (Length in the current scale drawing)
Given that the length in the current drawing is 8 boxes and the scales' relationships are 1 box = 3 inches and 1 box = 6 inches, we can calculate the ratio as follows:
Ratio = (Length in new drawing) / (8 boxes) = (1 box/6 inches) / (1 box/3 inches)
Now, simplify the ratio:
Ratio = (1/6) / (1/3) = (1/6) × (3/1) = 1/2
So, the ratio between the two scales is 1/2.
To find the length in boxes of the new scale drawing, we multiply the ratio by the length in the current drawing:
Length in new drawing = (Length in the current drawing) × (Ratio) = 8 boxes × (1/2) = 4 boxes
Therefore, the length in boxes of the new scale drawing will be 4 boxes.
If the original scale is 1 box = 3 inches and the length shown is 8 boxes, the length would be 8 boxes x 3 inches/box = 24 inches in the original scale drawing.
To convert to a new scale of 1 box = 6 inches, we need to find the length in boxes in the new scale drawing.
The new scale is twice the size of the original scale, so the length in boxes in the new scale drawing would be 24 inches / 6 inches/box = 4 boxes.
Therefore, the length in boxes of the new scale drawing would be 4 boxes.
Given that the length of the bureau drawer in the current scale drawing is 8 boxes and the scale is 1 box = 3 inches.
To convert the scale to 1 box = 6 inches, we need to double the size of each box.
So, 1 box in the new scale = 2 boxes in the current scale = 2 x 3 inches = 6 inches.
Therefore, the length of the bureau drawer in the new scale drawing will be 8 boxes x 2 = 16 boxes.