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Mathematics > Standard Multiple Choice

The odometer of a new automobile functions improperly and registers only miles for every miles driven. If the odometer indicates miles, how many miles has the automobile actually been driven?

Correct!

Explanation

In this problem, you are told that the odometer registers only miles for every miles driven. So the ratio of miles registered to miles driven is to or . This can be expressed as

If the odometer indicates miles, the actual miles can be found using using the above relationship as follows:

So if the odometer indicates miles, the actual number of miles driven is .

How to Avoid Errors When Working with Ratios

The most important thing with ratios is to be consistent in the way you set them up. If you mix up the terms, you won’t get the correct answer. For instance, if you put the registered mileage in the numerator of one ratio but the actual mileage in the numerator of the other ratio, you will come up with a wrong answer: