fatihaysu wrote:
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 and 290/11.5
B. 295/12 and 285/11.5
C. 285/12 and 295/12
D. 285/12.5 and 295/11.5
E. 295/12.5 and 285/11.5
In solving this problem we must remember that we are given a rate in miles per gallon. It follows that:
Rate = Distance/Gallons
We are given that she drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. We are being asked to determine a possible range for Cindy’s rate. Thus, we really are trying to determine the maximum value for her rate (the largest distance traveled divided by the smallest number of gallons used) and the minimum value for her rate (the smallest distance traveled divided by the largest number of gallons used).
Let’s first determine the minimum and maximum distance. We know that she drove 290 miles, rounded to the nearest ten miles. Thus, we first determine what values will round to 290 when rounded to the nearest 10 miles. This means the actual number of miles driven can be any number from 285 to a number that is almost 295.
So we can say the minimum distance is 285 miles and the maximum distance is (almost) 295 miles.
Next, we determine the minimum and maximum number of gallons used. We know that she used 12 gallons of gas, rounded to the nearest gallon. It follows that the actual number of gallons of gas used can be any number from 11.5 to a number that is almost 12.5.
So we can say the minimum number of gallons is 11.5 and the maximum number of gallons is (almost) 12.5.
Using the formula Rate = Distance/Gallons we see that the maximum rate is the maximum miles divided by the minimum gallons, which is 295/11.5.
Similarly, the minimum rate is the minimum miles divided by the maximum gallons, or 285/12.5.
We can see that our maximum and minimum rates are exactly those given in answer choice D.
Answer D
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