Question
A building is 32 feet tall but the width is unknown, A model of the building is 10 inches tall and 15 inches wide. What is the width of the actual building?
Answers
GPT 3.5
To solve this problem, we can set up a proportion between the height and width of the model and the actual building.
Let x be the width of the actual building.
According to the proportion, we have:
(Height of the actual building) / (Width of the actual building) = (Height of the model) / (Width of the model)
Substituting in the given values:
32 feet / x = 10 inches / 15 inches
To convert the units, we need to choose either inches or feet for both numerator and denominator. Let's convert everything to inches:
32 feet = 32 * 12 inches = 384 inches
Simplifying the proportion, we get:
384 inches / x = 10 inches / 15 inches
Cross-multiplying gives:
384 inches * 15 inches = 10 inches * x
5760 inches^2 = 10 inches * x
Now we can solve for x by dividing both sides of the equation by 10 inches:
x = 5760 inches^2 / 10 inches
x = 576 inches
Therefore, the width of the actual building is 576 inches.
Let x be the width of the actual building.
According to the proportion, we have:
(Height of the actual building) / (Width of the actual building) = (Height of the model) / (Width of the model)
Substituting in the given values:
32 feet / x = 10 inches / 15 inches
To convert the units, we need to choose either inches or feet for both numerator and denominator. Let's convert everything to inches:
32 feet = 32 * 12 inches = 384 inches
Simplifying the proportion, we get:
384 inches / x = 10 inches / 15 inches
Cross-multiplying gives:
384 inches * 15 inches = 10 inches * x
5760 inches^2 = 10 inches * x
Now we can solve for x by dividing both sides of the equation by 10 inches:
x = 5760 inches^2 / 10 inches
x = 576 inches
Therefore, the width of the actual building is 576 inches.