The total number of miles would have ranged between 284 and 295 i.e. 284 < x < 295 or 285 <= x <= 295 ; where x = miles
Likewise total number of miles would have ranged between 11.4 and 12.5 i.e. 11.4 < y < 12.5 or 11.5 <= y < = 12.4; where y = gallons
Your approach is correct, but I hope the OG doesn't say ranges between, instead of ranges from. Both convey different meanings.
Did you manage the answer with your approach?

Allen

Please provide the options, so that even moderators of this forum can help us.

I will be grateful, if you can provide the complete explanation.

284 rounds down (to the nearest 10) to 280, not 290

The range of miles per gallon would be

285/12.4 (the smallest possible number) to . . .

294/11.5 (the largest possible number

What are the choices??

The complete question:

On a recent trip, Cindy drove her car for 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:

a) 290/12.5 and 290/11.4

b) 295/12 and 284/11.4

c) 284/12 and 295/12

d) 284/12.5 and 295/11.4

e) 295/12.5 and 284/11.4






The book answer is as follows:

The lowest number of miles per gallon can be calculated using the lowest possible miles and the highest amount of gasoline. Conversely, the highest number of miles per gallon can be calculated using the highest possible miles and the lowest amount of gasoline.

Since the miles are rounded to the nearest 10 miles, they can range anywhere from 284 miles to 295 miles. Since the gallons of gasoline are rounded to the nearest gallon, they can range anywhere from 11.4 gallons to 12.5 gallons. Therefore, the following calculations can be set up.

Lowest number of miles per gallon = 284/12.5

Highest number of miles per gallon = 295/11.4

The correct answer is D.


My problem is that I'm still not tracking how 284 rounds up to 290 and how 11.4 rounds up to 12.