SOLUTION: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol. 4$ per gallon 5$ per gallon 7$ per gallon 8$

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A reduction in the price of petrol by 10% enables a motorist to buy 5 gallons more for$180. Find the original price of petrol. 4$ per gallon 5$ per gallon 7$ per gallon 8$       Log On


   

Question 1206727: 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.

4$ per gallon
5$ per gallon
7$ per gallon
8$ per gallon
Found 3 solutions by MathLover1, josgarithmetic, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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let's the original price of petrol be p and the the number of gallons purchased be n
if he paid full price, the number of gallons would be n=180%2Fp...eq.1
if the price is reduced 10%, the new price of petrol becomes 0.9p, and the new number of gallons purchased becomes n+%2B+5

so, with reduced price we have:
180+=+0.9p+%2A+%28n+%2B+5%29...substitute n
180+=+0.9p+%2A+%28180%2Fp+%2B+5%29
180+=+0.9p+%2A+%28%28180%2B5p%29%2Fp+%29
180+=+0.9%2A+%28180%2B5p%29
180+=+4.5p+%2B+162
4.5p+=180-+162
4.5p+=18
p=18%2F4.5
p=4

answer:
the original price of petrol is $4 per gallon


Answer by josgarithmetic(39620) About Me  (Show Source):
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PRICE%2AQUANTITY=COST 
PRICE           QUANTITY gallons        COST dollars

 p                  180/p                 180

 0.9p            180/(0.9p)               180

difference            5

highlight_green%28180%2F%280.9p%29-180%2Fp=5%29


200%2Fp-180%2Fp=5
20%2Fp=5
highlight%28p=4%29

Answer by greenestamps(13200) About Me  (Show Source):
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A very different solution method than shown by the other tutors....

Let x be the number of gallons he can buy at the regular price; then x+5 is the number of gallons he can buy at the reduced price.

The cost of (x+5) gallons at 90% of the original price is equal to the cost of x gallons at the original price:

.9%28x%2B5%29=x
9%28x%2B5%29=10x
9x%2B45=10x
x=45

For $180, he could buy 45 gallons. The original price per gallon was $180/45 = $4.

ANSWER: $4