nkmungila wrote:
Due to a sudden 20% increase in price, one is now able to buy 4 gallons lesser oil than earlier on the same expenditure of
$600. What is the dollar increase in the price of oil per gallon?
A. $2
B. $5
C. $10
D. $20
E. $25
Test the answers. The equation for this one was taking too long. Backsolving was quick.
(Price per gallon P) * (# of gallons Q) = Total cost
Q = Total cost/price per gallon
1) Find original price from given dollar increase
2) Find original # of gallons by dividing $600 by old price per gallon
3) Find new price
= (1.2)($old), OR
($Old price + added $ increase)
4) Find new # gallons. Divide 600 by new price
Answer C) $10
$10 is both the dollar increase in price and a .20 increase of original price, x
Original price:
$10 = .2x = \(\frac{10}{.2} = $50\)
Original number of gallons:
\(\frac{$600}{$50PerGal} = 12\) gallons
New price: $50 + $10 (or 1.2 * $50) = $60
New number of gallons
\(\frac{$600}{$60per} = 10\) gallons
12 - 10 = 2 fewer gallons now. Too small. That means the dollar price increase is too large. To increase quantity, decrease price.
Try B) $5
$5 = .2x
Original price:
\(\frac{$5}{.2} = $25\)
Original quantity:
\(\frac{$600}{$25per} = 24\) gallons
New price: (1.2)($25) or ($25 + $5) = $30
New quantity:
\(\frac{$600}{$30per} = 20\) gallons
24 - 20 = 4 gallons. Correct
Answer B
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