An art student wants to make a model of the classroom. The length of the classroom is 2.4 times its width. The length of the student’s model is 42 in. What should the width of the model be?
Let's assume the width of the classroom is x.
Therefore, the length of the classroom is 2.4 times the width, which is 2.4x.
According to the information given, the length of the student's model is 42 in.
Since the length of the model is in proportion to the length of the classroom, we can write the equation:
(Length of the model)/(Length of the classroom) = (Width of the model)/(Width of the classroom)
Substituting the given values, we get:
42/2.4x = w/x
Simplifying the equation, we get:
42/2.4 = w
17.5 = w
Therefore, the width of the model should be 17.5 inches.
To find the width of the model, we need to determine the width of the actual classroom.
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. Therefore, the length of the classroom can be expressed as 2.4w.
However, we are given the length of the student's model, which is 42 inches.
Since the dimensions of the actual classroom and the model are proportional, we can set up a proportion to find the width of the model.
The proportion can be written as:
Width of the model / Length of the model = Width of the classroom / Length of the classroom
Let's substitute the given values:
x / 42 = w / (2.4w)
To solve for x, we can cross-multiply the equation:
x * (2.4w) = 42 * w
Simplifying, we get:
2.4wx = 42w
Now, we can cancel out the common factor of "w" on both sides:
2.4x = 42
To isolate "x", we divide both sides by 2.4:
x = 42 / 2.4
Evaluating the expression, we find:
x ≈ 17.5
Therefore, the width of the model should be approximately 17.5 inches.