Video: SAT Practice Test 1 • Section 4 • Question 32

A model for a university campus is created using a scale of 1 inch to 34 feet. If the university’s administration building is actually 85 feet tall, what is the height of the building in the model in inches?

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Video Transcript

A model for a university campus is created using a scale of one inch to 34 feet. If the university’s administration building is actually 85 feet tall, what is the height of the building in the model in inches?

We get some key information in the question. And the first bit being that one inch on the model is equal to 34 feet in real life and that’s the scale. And then, we’re also told that university’s administration building is actually 85 feet tall. So writing this down, we’ve got that 34 feet gives us one inch and that’s our scale. So 34 feet in real life equals one inch on the model. So if we’re wanting to find out what 85 feet is equal to in our model, then what we’re gonna need to do first of all is find out what one foot is equal to.

And to do that, what we’re gonna do is divide each side of our ratio by 34. And that’s cause if we have 34 feet and we divide it by 34, we get one foot. And we also know that whatever we do to one side, we’re gotta do to the other side. So we’ve also gotta divide one inch by 34. So therefore, when we do that, we can say that one over 34 inches on our model represent one foot in real life. And I’m gonna keep that as a fraction just for the moment because it keeps our accuracy.

So now, if we want to work out how many inches on our model is gonna represent 85 feet in real life, what we’re gonna do is multiply each side of our ratio by 85. And we want 85 foot because that’s the height of the university’s administration building. So therefore, we can say that 85 foot in real life, so 85 foot the height of the administration building, is gonna be represented by 85 multiplied by one over 34 inches on the model.

So when we multiply 85 by one over 34, we’re gonna get 85 over 34. So it’s gonna be 85 over 34 inches, which is gonna give us an answer of 2.5 inches. And we could’ve worked this out using our calculator. But also, we can work it out using a mental method. So if we’re using a mental or written method, we can work it out like this, which is two multiplied by 34 is 68 because we wanna see how many 34s go into 85. Then, we do 85 minus 68 which is 17. So therefore, we can say that it’s two and 17 over 34. Well, 17 over 34 is the same as a half. So we get the answer of two and a half or 2.5 for our 2.5 inches.

So therefore, we can say that the height of the university’s administration building in the model if the actual building is 85 feet tall is going to be 2.5 inches.