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Bunuel
A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?

\(\text{mpg} = \frac{\text{distance (miles)}}{\text{volume (gallons)}}\)

\(\frac{270}{18} = 15\text{mpg}\\\\
\frac{270}{10} = 27\text{mpg}\)
\(27 - 15 = 12\)

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Mileage = \(\frac{distance}{gallons of fuel used}\)

original mileage of truck = \(\frac{270}{18}\) = 15 miles/gallon

new mileage of truck = \(\frac{270}{10}\) = 27 miles/gallon

so the mileage must be increased by 27 - 15 = 12 miles/gallon
Correct Answer - C
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In 18 gallons= 270 miles, therefore 1 gallon= 270/18 miles, thus in 10 gallons = (270*10)/18= 150 miles. Diffrential is 270-150= 120. Thus to cover 120 miles in 10 gallons you need 120/10= 12 miles extra mileage to be kicked in for us to cover 270 miles
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Bunuel
A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?

A. 8
B. 9
C. 12
D. 15
E. 27

\(\frac{270}{10} - \frac{270}{18}\)

\(= 27 - 15\)

= 12, Answer must be (C)
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Bunuel
A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?

A. 8
B. 9
C. 12
D. 15
E. 27


The current rate is 270/18 = 15 miles per gallon.

The new rate would need to be 270/10 = 27 miles per gallon.

So the truck’s fuel mileage must be increased by 27 - 15 = 12 mpg.

Answer: C
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CONCEPT: Percentage
-Percentage increase/decrease.
- For inversely proportional quantities, if there an increase in one of the quantities by a fraction of x/y(x/y*100 as a
percentage), then the corresponding decrease in the other quantity is x/(x+y)
-If there is a decrease in one of the quantities by a fraction of x/y, then the corresponding increase in the
other quantity is x/|(y-x)|.

SOUTION: Current mileage of the truck = Distance/Vol. of fuel used to cover that distance
=270/18 = 15 miles/gallon
Decrease in volume of fuel as a fraction = 18-10/18 = 4/9.
Corresponding increase in mileage of the vehicle = 4/(9-4) = 4/5
Thus, mileage needs to increase by 4/5 of 15 =4/5*15 =12 miles/gallon.(C)

Hope this helps :) Keep studying :thumbsup:
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Bunuel
A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?

A. 8
B. 9
C. 12
D. 15
E. 27
Original Mileage is \(\frac{270}{18} = 15\)
Increased Mileage is \(\frac{270}{10} = 27\)

So, Mileage must be increased by 12 miles/gallon, Answer must be (C)
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