trip maths

[francoisph]

hi guys

please any ideas?

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?

why it is D) 285/12.5 AND 295/11.5
??

WHY rounded the nearest 10 means? 5

thks

[albatross86]

Rounding to the nearest tens means that we are trying to take any value to the nearest multiple of 10.

eg. 9 rounds off to 10. 265 rounds off to 270. 1433 rounds off to 1430

Rounding to the nearest gallon, would mean that we want an integer value, so we round to the nearest integer.

eg. 1.5 rounds off to 2, 66.7 rounds off to 67, 9311.2 rounds off to 9311


The problem here is asking you to do the reverse of this process. They are giving you the rounded off value and asking you to predict the range of values that it could have been.

If she drove 290 miles rounded to the nearest 10 miles, it could have been that she had actually driven anywhere between 285 (inclusive) and 295 miles (exclusive)

Similarly, if she used 12 gallons rounded to the nearest gallon, it could have been anywhere between 11.5 (inclusive) and 12.5 (exclusive)

The biggest fraction is the greatest numerator upon lowest denominator, and vice versa for smallest

Thus, 295/11.5 is max, and 285/12.5 is min.



Remember, rounding off is just a convention, just a mathematical rule that is used, so just follow it blindly that 0 to 4 rounds down and 5 to 9 rounds up. Good luck!