7
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Scale: 1box = 4 inches
Ana Maria needs to convert this scale drawing from a scale of 1box = 4 inches to a scale of 1hnx = 2 inches. The width in the scale drawing shown is 3 boxes. What will be the width in boxes of the new drawing?
(1 point)
To convert the scale from 1 box = 4 inches to 1 hnx = 2 inches, we need to determine the conversion factor between boxes and hnx.
Since 1 box is equal to 4 inches, and 1 hnx is equal to 2 inches, the conversion factor can be calculated as:
1 box / 4 inches = x hnx / 2 inches
Cross multiplying the terms:
2 inches * 1 box = 4 inches * x hnx
2 boxes = 4 inches * x hnx
To solve for x:
x hnx = 2 boxes / 4 inches
x hnx = 1/2
Therefore, the conversion factor from boxes to hnx is 1/2.
Now, we need to find the width in boxes of the new drawing. The width in the scale drawing shown is 3 boxes. To convert this width to the new scale, we can multiply by the conversion factor:
Width in hnx = Width in boxes * Conversion factor
Width in hnx = 3 boxes * 1/2
Width in hnx = 1.5 boxes
Therefore, the width in boxes of the new drawing will be 1.5 boxes.
To convert from a scale of 1 box = 4 inches to a scale of 1 hnx = 2 inches, we need to find the ratio of the new scale to the old scale.
The old scale is 1 box = 4 inches, and the new scale is 1 hnx = 2 inches.
To find the ratio, we divide the new scale by the old scale:
(1 hnx / 2 inches) / (1 box / 4 inches)
This simplifies to:
(1 hnx / 2 inches) * (4 inches / 1 box)
Now, we can multiply the widths of the scale drawing by this ratio to find the width of the new drawing in boxes.
The width in the scale drawing is 3 boxes, so we multiply this by the ratio:
3 boxes * (1 hnx / 2 inches) * (4 inches / 1 box)
The "boxes" units cancel out, leaving us with:
3 * 1 hnx * 4 inches / 2 inches
Simplifying further:
3 * 2 hnx * 2 inches
Finally, we can multiply:
6 hnx * 2 inches
The width of the new drawing in boxes is 6.
To find the width in boxes of the new drawing, we can use the concept of ratios.
First, let's find the width in inches of the original scale drawing. Since 1 box in the original scale drawing represents 4 inches, the width in inches would be 3 boxes multiplied by 4 inches per box, which is 12 inches.
Now, we can use the concept of ratios to find the width in boxes of the new drawing. We know that in the new scale, 1hnx represents 2 inches. So, to find the width in boxes of the new drawing, we can set up the following ratio:
Width in inches of the original drawing : Width in inches of the new drawing = Width in boxes of the original drawing : Width in boxes of the new drawing
12 inches : 2 inches = 3 boxes : Width in boxes of the new drawing
Simplifying the ratio, we get:
6 : 1 = 3 : Width in boxes of the new drawing
Cross multiplying, we get:
6 * Width in boxes of the new drawing = 3 * 1
6 * Width in boxes of the new drawing = 3
Dividing both sides by 6, we get:
Width in boxes of the new drawing = 3 / 6
Simplifying, we get:
Width in boxes of the new drawing = 1/2
Therefore, the width in boxes of the new drawing is 1/2.