On a recent trip, Cindy drove her

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

2 Explanations

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Cydney Seigerman, Magoosh Tutor

Hi Gessika :)

Happy to help! For this question, we need to find the range for the actual miles per gallons based on the estimations given. Based on the given information, we can conclude that she drove between 285 and 295 miles and used between 11.5 and 12.5 gallons of gas. To determine the range of miles/gallons, we need to find the maximum and minimum possible values. To find the minimum value, we will want to have the smallest numerator possible and the largest denominator. On the other hand, to find the maximum value, we'll want the largest numerator divided by the smallest denominator. For that reason we divide 285 miles/ 12.5 gallons to find the minimum value of the range and 295 miles / 11.5 gallons to find the maximum value of the range. :)

I hope that helps!

May 25, 2016 • Comment

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Mike McGarry, Magoosh Tutor

Aug 17, 2015 • Comment

Gessika M

Hi! Can you explain why you divided the smallest # of mileage by the largest gal (i.e. 285.5/12.5 instead of 285.5/11.5)? Thanks.

May 19, 2016 • Reply

Derrick Haynes

Hi if Cindy drove her car 295 miles, why wouldn't the nearest 10 miles be 300 miles. Why don't we round up in this case? Thanks!

Jul 15, 2017 • Reply

Sam Kinsman

You're right, Derrick - if she drove 295 miles, that would be rounded up to 300. However, there's a reason that we use 295 instead of 294.

If Cindy drove just a tiny bit less than 295 miles - her trip would be rounded down to 290 miles. So if, for example, she drove 294.99999 miles, that would be rounded down to 290. So the maximum distance she could have driven is 294.99999 miles (with an infinite number of 9s after the decimal). But that's a very tedious number to work with! So instead, we can just approximate it to 295.0.

I hope that helps explain! :)

Jul 20, 2017 • Reply