Use the image to answer the question.
8
4
e / 1 * box = 3in
Convert this scale drawing of a bureau drawer so that it has a scale of 1hnx = 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 convert the scale drawing to a scale of 1hnx = 6 inches, we need to divide the original length in boxes by the scale factor of the new scale.
The original length in boxes is 8.
Dividing 8 by the scale factor of 6 inches gives us the length in boxes of the new scale drawing:
8 boxes / 6 inches = 1.333 boxes (rounded to 3 decimal places).
Therefore, the length in boxes of the new scale drawing will be approximately 1.333 boxes.
To convert the scale drawing to a scale of 1hnx = 6 inches, we need to determine the ratio between the current scale and the new scale.
Given that e / 1 * box = 3in, we can write the following equations:
e / 1 * box = 3in
1hnx / 6in = e / 1 * box
To find the length in boxes of the new scale drawing, we can use the following steps:
Step 1: Solve for "e" by multiplying both sides of the second equation by 6in:
1hnx = e * 6in / 1 * box
Step 2: Now, substitute the value of "e" in the first equation:
e / 1 * box = 3in
(e * 6in / 1 * box) / 1 * box = 3in
Simplify:
e * 6in = 3in * 1 * box
Step 3: Divide both sides by 6in to isolate "e":
e = (3in * 1 * box) / 6in
Simplify:
e = 3in / 2
Step 4: Substitute the value of "e" in the second equation:
1hnx / 6in = (3in / 2) / 1 * box
1hnx / 6in = 3in / (2 * 1 * box)
Step 5: Multiply both sides of the equation by 6in to isolate "1hnx":
(1hnx / 6in) * 6in = (3in / (2 * 1 * box)) * 6in
1hnx = (3in * 6in) / (2 * 1 * box)
Simplify:
1hnx = 18in / (2 * 1 * box)
Step 6: Simplify the expression:
1hnx = 9in / (1 * box)
Therefore, in the new scale drawing with a scale of 1hnx = 6 inches, the length in boxes will be 9 boxes.
To answer this question, we need to understand that the current scale is 1 box = 3 inches and we want to convert it to a new scale of 1hnx = 6 inches.
First, let's find the current length of the bureau drawer in inches. We are given that the length in the scale drawing is 8 boxes, and using the current scale of 1 box = 3 inches, we can calculate the current length in inches:
Current Length = 8 boxes * 3 inches/box = 24 inches
Now, we can use the new scale to find the length in boxes of the new scale drawing. Since the new scale is 1hnx = 6 inches, we can set up a proportion to find the length in boxes:
Current Length (inches) / Current Scale (inches/box) = New Length (inches) / New Scale (inches/box)
Plugging in the values we know:
24 inches / 3 inches/box = New Length (inches) / 6 inches/box
Simplifying the proportion:
8 boxes = New Length (inches) / 6 inches/box
To find the length in boxes of the new scale drawing, we need to isolate New Length. Multiply both sides of the equation by 6 inches/box:
8 boxes * 6 inches/box = New Length (inches)
48 inches = New Length (inches)
Therefore, the length in boxes of the new scale drawing is 48 inches.