dancinggeometry wrote:
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 x(2^1/2) - x 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
Lets y be the number of days until prices are equal.
The end price of corn = 3.2 + 5xy
The end price of wheat = 5.8 - x(1.4-1) = 5.8 - 0.4xy
The two end prices are equal -> 3.2 +5xy = 5.8 - 0.4xy
From here we get that 5.4xy = 2.6, or y = 2.6/5.4x or 26/54x
Replace y in first equation and you get 3.2 + 5x(26/54x), cross the x and you get approximately 3.2 + 2.4 = $5.6
Check price for 2nd equation = 5.8 - 0.4x(26/54X), cros x and you get 5.8 - 0.2 = $5.6
I got to y = 2.6/5.4X via a number of simple methods and it took me 4-5 mins to realize this is all I needed:))