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 5x5x cents per day while the price of wheat is decreasing at a constant rate of 2√∗x−x2∗x−x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat? Choose one:
A) $4.50
B) $5.10
C) $5.30
D) $5.50
E) $5.60
Let yy be the # of days when these two bushels will have the same price.   First let's simplify the formula given for the rate of decrease of the price of wheat: 2√∗x−x=1.41x−x=0.41x2∗x−x=1.41x−x=0.41x, this means that the price of wheat decreases by 0.41x0.41x cents per day, in yy days it'll decrease by 0.41xy0.41xy cents;   As price of corn increases 5x5x cents per day, in yy days it'll will increase by 5xy5xy cents;   Set the equation: 320+5xy=580−0.41xy320+5xy=580−0.41xy, solve for xyxy --&gt; xy=48xy=48;   The cost of a bushel of corn in yy days (the # of days when these two bushels will have the same price) will be 320+5xy=320+5∗48=560320+5xy=320+5∗48=560 or $5.6.   Answer: $5.60.
<result>E</result>
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 5x5x cents per day while the price of wheat is decreasing at a constant rate of 2√∗x−x2∗x−x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?