Dustin has a scale model of his Dad's truck. The length of the scale model is 2 inches and its width is 1 inch. If the actual truck measures 11 feet long, how wide is the actual tr... Dustin has a scale model of his Dad's truck. The length of the scale model is 2 inches and its width is 1 inch. If the actual truck measures 11 feet long, how wide is the actual truck?
Understand the Problem
The question describes a scale model of a truck and asks to determine the actual width of the truck given the length of the actual truck and the dimensions of the scale model. We need to find the ratio between the model and the actual truck using the lengths, and then apply that ratio to the width of the model to find the actual width of the truck.
Answer
D. 5.5 feet
Answer for screen readers
D. 5.5 feet
Steps to Solve
- Find the scale ratio
The length of the scale model is 2 inches, and the actual truck is 11 feet long. We can set up a ratio to represent the scale:
$ \text{Scale ratio} = \frac{\text{Model length}}{\text{Actual length}} = \frac{2 \text{ inches}}{11 \text{ feet}} $
- Determine the actual width
The width of the scale model is 1 inch. To find the actual width of the truck, we can use the scale ratio:
$ \frac{\text{Model width}}{\text{Actual width}} = \frac{2 \text{ inches}}{11 \text{ feet}} $
Let $x$ be the actual width of the truck in feet. Then:
$ \frac{1 \text{ inch}}{x \text{ feet}} = \frac{2 \text{ inches}}{11 \text{ feet}} $
Cross-multiply to solve for $x$:
$ 2x = 11 $
$ x = \frac{11}{2} = 5.5 $
Therefore, the actual width of the truck is 5.5 feet.
D. 5.5 feet
More Information
Scale models are used to represent larger or smaller objects, maintaining accurate proportions. The ratio between corresponding dimensions of the model and the actual object is constant.
Tips
A common mistake is failing to set up the proportion correctly. Make sure corresponding dimensions are in the correct positions in the ratios. Another common mistake is to not use the same units, but in this problem, the question gives us the answer options in feet, so it's easier to compute the answer directly.
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