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
A reduction in the price of petrol by 10% enables a motorist
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Original:
x gallons * $ n = 180
Reduced New:
(x+5) gallons * $(10.1)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
x gallons * $ n = 180
Reduced New:
(x+5) gallons * $(10.1)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
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Let P = the original price per gallon.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. $4
OAE
So, if the price is reduced 10%, the new price is 0.9P
IMPORTANT: # of gallons purchased = ($ spent)/(price per gallon)
We can start with the following word equation:
(# of gallons purchased for $180 at original price) + 5 = (# of gallons purchased for $180 at reduced price)
So, ($180/P) + 5 = ($180/0.9P)
At this point, you might choose to plug in the answer choices, or you can solve the equation. Let's solve the equation. . .
Given: ($180/P) + 5 = ($180/0.9P)
Eliminate the fractions by multiplying both sides by 9P: (180)(9) + 45P = (180)(10)
So, 45P = 180
P = 4
Answer: E
Cheers,
Brent
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We can plug in the answers, which represent the original price.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
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 = 4036 = 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 = 5045 = 5 gallons.
Success!
The correct answer is E.
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Followed here and elsewhere by over 1900 testtakers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia  a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua  a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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