An art student wants to make a model of a rectangular classroom. The length of the classroom is 2.4 times it's width. The length of the model is 42 in. What should the width of the model be?
17.5 in
20.5 in
83.6 in
100.8 in
Let's say the width of the rectangular classroom is represented by "w". Since the length is 2.4 times the width, the length would be 2.4w.
We're given that the length of the model is 42 inches, which represents 2.4w.
So, 2.4w = 42.
To solve for w, divide both sides of the equation by 2.4:
w = 42 / 2.4 = 17.5 inches.
Therefore, the width of the model should be 17.5 inches.
To find the width of the model, we can start by finding the length of the actual classroom.
Let's assume that the width of the classroom is x.
According to the given information, the length of the classroom is 2.4 times its width, which means:
Length = 2.4 * Width
Substituting the value of x, we have:
Length = 2.4 * x
Since the actual length of the classroom is not given, we can't find the exact value of x. However, we can solve for the width of the model using the given information.
We know that the length of the model is 42 inches.
So, Length (model) = 42 inches
Since the length of the model is a scaled-down version of the actual length, we can write:
Length (model) = Length (actual) / Scale factor
Substituting the values, we have:
42 = Length (actual) / Scale factor
Let's assume the scale factor is y.
So, 42 = Length (actual) / y
We already found that the length (actual) = 2.4 * Width. Substituting this value, we have:
42 = (2.4 * Width) / y
To find the width of the model, we need to find the value of y.
To do that, we can rearrange the equation:
42 * y = 2.4 * Width
Dividing both sides by 2.4, we have:
(42 * y) / 2.4 = Width
Simplifying further, we have:
Width = 17.5y
So, the width of the model should be a multiple of 17.5 inches.
Based on the available options, the width of the model should be 17.5 in.
To find the width of the model, we need to first find the actual width of the classroom and then scale it down to the size of the model.
Let's assume the width of the classroom is 'w'. According to the given information, the length of the classroom is 2.4 times its width, so the length of the classroom would be 2.4w.
Since we know the length of the model is 42 inches, we can set up the following equation:
2.4w = 42
To find the value of 'w', we can divide both sides of the equation by 2.4:
w = 42 / 2.4
Using a calculator, we can solve this equation to find that the actual width of the classroom is approximately 17.5 inches.
Now, we need to find the width of the model. Since we are scaling down from the actual dimensions to the model dimensions, we need to find the scale factor. The scale factor is equal to the length of the model divided by the length of the actual object. In this case, the scale factor is:
scale factor = width of the model / width of the classroom
Let's denote the width of the model as 'm'. Using the scale factor, we can set up the following equation:
scale factor = m / w
Since we know the length of the model (42 inches) and the width of the classroom (17.5 inches), we can substitute these values into the equation:
scale factor = m / 17.5
To find the value of 'm', we can rearrange the equation:
m = scale factor * 17.5
To determine the width of the model, we need to choose one of the answer options and check if it satisfies the equation. Let's try the first option, 17.5 in:
m = 1 * 17.5 = 17.5
Since the first option matches our calculations, the width of the model should be 17.5 inches. Therefore, the correct answer is 17.5 in.