Final answer:
To find the actual length of a car based on a 14-inch model with a scale of 2 1/4 inches = 3 feet, set up a proportion and cross-multiply. Convert 14 inches to feet and use the scale in feet to solve, resulting in an actual car length of approximately 99.556 feet.
Step-by-step explanation:
The model of a car uses a scale of 2 1/4 inches = 3 feet. This means that for every 2 1/4 inches of the model, the actual car is 3 feet in length. To find the actual length of the car based on a 14-inch model, we need to set up a proportion.
First, we convert the scale to a consistent unit. Since we are measuring the actual car in feet, let's convert 2 1/4 inches to feet. There are 12 inches in a foot, so 2 1/4 inches is 2.25/12 = 0.1875 feet.
Next, we set up our proportion using the scale:
- 2 1/4 inches (or 0.1875 feet) : 3 feet
- 14 inches : x feet
We then convert 14 inches to feet, which is 14/12 feet or about 1.1667 feet.
Now, our proportion looks like this:
0.1875 feet : 3 feet = 1.1667 feet : x feet
To find x, we cross-multiply and solve for x:
(0.1875 feet)(x feet) = (1.1667 feet)(3 feet)
x = (1.1667 feet * 3 feet) / 0.1875 feet
x = 18.667 / 0.1875
x = 99.556 feet
So, the actual length of the car is 99.556 feet.