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07 Jun 2024, 11:25
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An experimental vehicle averages \(x\) miles per gallon when driven in the city and \(2x\) miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of \(x\)?
A. 14
B. 16
C. 18
D. 20
E. 28
A. 14
B. 16
C. 18
D. 20
E. 28
07 Jun 2024, 11:25
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Official Solution:
An experimental vehicle averages \(x\) miles per gallon when driven in the city and \(2x\) miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of \(x\)?
A. 14
B. 16
C. 18
D. 20
E. 28
Vehicle averaging \(x\) miles per gallon means 1 gallon drives \(x\) miles.
Total miles driven: 120 (city) + 300 (highway) = 420 miles.
In the city, the vehicle uses (120 miles) / (\(x\) mpg) gallons.
On the highway, it uses (300 miles) / (\(2x\) mpg) gallons.
The average miles per gallon (miles/gallon), would be the total miles driven divided by the total gallons used, hence we'd have:
\(\frac{420}{\frac{120}{x} + \frac{300}{2x}}=28\)
\(\frac{420}{\frac{120}{x} + \frac{150}{x}}=28\)
\(\frac{420}{\frac{270}{x}}=28\)
\(\frac{14x}{9}=28\)
\(x=18\)
Answer: C
An experimental vehicle averages \(x\) miles per gallon when driven in the city and \(2x\) miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of \(x\)?
A. 14
B. 16
C. 18
D. 20
E. 28
Vehicle averaging \(x\) miles per gallon means 1 gallon drives \(x\) miles.
Total miles driven: 120 (city) + 300 (highway) = 420 miles.
In the city, the vehicle uses (120 miles) / (\(x\) mpg) gallons.
On the highway, it uses (300 miles) / (\(2x\) mpg) gallons.
The average miles per gallon (miles/gallon), would be the total miles driven divided by the total gallons used, hence we'd have:
\(\frac{420}{\frac{120}{x} + \frac{300}{2x}}=28\)
\(\frac{420}{\frac{120}{x} + \frac{150}{x}}=28\)
\(\frac{420}{\frac{270}{x}}=28\)
\(\frac{14x}{9}=28\)
\(x=18\)
Answer: C
27 Oct 2024, 16:40
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