Problem Solving

A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol?

A. $11
B. $5
C. $45
D. $400
E. $4

OAE

Original:

x gallons * $ n = 180

Reduced New:

(x+5) gallons * $(1-0.1)n = 180

(x+5)(0.9n) = 180

0.9xn + 4.5n = 180

Substitute original equation xn = 180

0.9xn + 4.5n = 180
0.9(180) + 4.5n = 180
162 + 4.5n = 180
4.5n = 180 - 162 = 18
n = 18/4.5 = $4

guerrero wrote:A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for $180. Find the original price of petrol?

A. $11
B. $5
C. $45
D. $400
E. $4

OAE

We can plug in the answers, which represent the original price.
The correct answer choice is almost certainly a factor of $180 -- B, C, or E.
The price in answer choice C -- $45 per gallon -- seems way too high.

Answer choice B: 5
Number of gallons that can be purchased at the original price = 180/5 = 36.
Discounted price = 5 - .1(5) = 4.5.
Number of gallons that can be purchased at the discounted price = 180/4.5 = 40.
Increase in purchasing power = 40-36 = 4 gallons.
Doesn't work: the increase in purchasing power must be 5 gallons.
Eliminate B.

Answer choice E: 4
Number of gallons that can be purchased at the original price = 180/4 = 45.
Discounted price = 4 - .1(4) = 3.6.
Number of gallons than can be purchased at the discounted price = 180/3.6 = 1800/36 = 50.
Increase in purchasing power = 50-45 = 5 gallons.
Success!

The correct answer is E.