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?
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.