Weighted Average

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Weighted Average

by awilhelm » Fri Jan 23, 2009 1:19 pm
A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. Acording to these rates, which of the following is the closest to the number of miles per gallon the car averages when driven 10 miles in the city and 50 miles on the highway?

a) 28
b) 30
c) 33
d) 36
e) 38

I have:

[ (25 mpg * 10 miles) + (40 mpg * 50 miles) ] / (10 + 50 miles)

(250 + 2000)/60

2250/60

37.5 miles per gallon, and therefore answer choice e.

OA is d. Where am I going wrong?
Source: — Problem Solving |

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by DanaJ » Fri Jan 23, 2009 1:34 pm

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by awilhelm » Fri Jan 23, 2009 1:52 pm
Thanks again!

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by awesomeusername » Fri Jan 23, 2009 2:28 pm
25mpg city
40mpg hwy

you traveled a total of 10 miles city, 50 miles hwy. So a total of 60 miles. We want final mpg. How many gallons of fuel were used?

10miles/(25miles/gal) = 10/25 gallons
50miles/(40miles/gal) = 50/40 gallons
Both added together are 33/20 gallons

so:

60 miles
----------
33/20 gallons

is

1200 miles/33 gallons = 36 and 12/33 miles/gallon. So 36 is the answer.