Problem Solving

... Cindy drove her car 290 miles, rounded to the nearest 10 miles, and...

--> so I thought that it could actually be 285 up to 294 miles

BUT: according to OG, it could be 285 up to 295

I don't understand, since 295 should be rounded up to 300?!

thx

Please make sure you post the full question always. You cannot expect the reader to go back to the OG and get the question.

Ok I just read the question.

You have to work with what is given.
Tha answer would be between the values given in D. So D is the correct answer. If you see clearly, no other answer can get you to the right answer.

I completely agree I am confused by the reasoning provided in the OG.
The question states, 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 cindy car got on this trip must have been between>
then comes answer choices.
None of which fit to my understanding of rounding..
The OG states the answer is found from making a range for miles and for gallons, then putting the lowest number of miles per gallon:
284/12.5
and the Highest number of miles per gallon:
295/11.4

I would think with rounding to the nearest 10 miles the range is from 285 to 294, otherwise if it is 295, then in the problem it should be rounded to 300, not down to 290 as it was in the problem.
Same problem with the min and max rounding they provided for gallons. I would have put the range at: 11.5 to 12.4

Writing in 2 days so really appreciate an experts view on this one !!

thank you

The point is that the OG is helping you learn to estimate. Your range of 285 to 294 is actually LESS accurate than the OG? Why? What is the answer if you were to round 294.99999999? That's NEARLY 295, so why not simplify and estimate with 295? Your answer of 294 is 1 full mile away from the max.

Obviously both numbers are estimates, but the OGs is in fact the closest estimate available.

Hope that helps...

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

A) 290/12.5 to 290/11.5

B) 295/12 to 285/11.5

C) 285/12 to 295/12

D) 285/12.5 to 295/11.5

E) 205/12.5 to 285/11.5

We round UP when we reach the HALFWAY point between two values.
Any value BELOW the halfway point is rounded DOWN.

290 miles, rounded to the nearest 10 miles:
285 ≤ m < 295.
Please note that 295 is the UPPER LIMIT.
Any value below 295 -- even 294.999 -- is rounded DOWN to 290.

12 gallons of gasoline, rounded to the nearest gallon:
11.5 ≤ g < 12.5.
Please note that 12.5 is the UPPER LIMIT.
Any value below 12.5 -- even 12.499 -- is rounded DOWN to 12.

Worst miles per gallon = (lower limit for miles)/(upper limit for gas) = 285/12.5.
Best miles per gallon = (upper limit for miles)/(lower limit for gas) = 295/11.5.
Thus, miles per gallon is between 285/12.5 and 295/11.5.

The correct answer is D.