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seemingly simple rounding question

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seemingly simple rounding question

by allenkt » Sat Apr 28, 2007 3:25 pm
OG 11, problem solving question #129 seems pretty straightforward:

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:


So it seems pretty simple. The lowest number is lowest possible miles / highest amount of gasoline and the highest number would be the highest possible miles / lowest possible gasoline.

Now comes my confusion. In answer guide it says,

"Since the miles are rounded to the nearest 10 miles they can range anywhere from 284 miles to 295 miles....gasoline can range from 11.4 miles to 12.5 gallons."

Rounding is pretty elementary but I've always learned that 284, rounded to the nearest 10, would round down to 280. Less than 5 rounds down and greater than or equal to 5 rounds up. So why isn't the range of miles between 285 - 294 and gasoline between 11.5 - 12.4? I don't understand why 284 rounds to 290 and 11.4 rounds to 12.
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by Cybermusings » Sun Apr 29, 2007 2:57 am
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?
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by f2001290 » Mon Apr 30, 2007 6:52 am
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.
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by Tame the CAT » Sun May 06, 2007 6:05 pm
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??
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by allenkt » Sun May 06, 2007 6:23 pm
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.
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