The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60
Friday, November 23, 2007
QUESTION # 2
Posted by Gaurav & Kunal at 11:45 PM
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2 Comments:
According to me the answer is (A) $4.50
I solved this one by elimination method, tell me if I go wrong.
I looked at the difference with the prices and the common price and found of feasible solutions.
4.50 - 3.20 = 1.30, hence at rate of 5x can take 13 or 26 days.
5.80 - 4.50 = 1.30 can also work for 13 or 26 days.
For the other options,
5.10 - 3.20 = 1.90 can work for 19 or 38 days
5.30 - 3.20 = 2.10 can work for 21 or 42 days
5.50 - 3.20 = 2.30 can work for 23 or 46 days
5.60 - 3.20 = 2.40 can work for 24 or 48 days
All the above cases fail to have multiples in cents which when added, add up 5.80, hence (A) is the answer.
Call y= the number of days prior to the day corn and wheat meet the same price
So we have 320 + 5xy= 58- - (x* square root 2 -x)y
--> we have xy = 260/(4+square root 2)
Substitute xy for 320 + 5xy, we have the price approximately is 5.6
So the answer is (E)
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