First, the 144 acres of grass will be eaten according to the equation 5*2*T + 8*1*T = 144.
Solving this equation for T, we find 18*T = 144, or T = 8 months of food are covered by the animals grazing on the rancher's pasture.
This means the farmer must buy feed corn for the remaining 12 - 8 = <<12-8=4>>4 months.
Next, the rancher's 8 sheep will require 4/2 = 2 bags of feed corn each, or 8*2 = <<8*2=16>>16 bags of feed corn in total for the 4 month period.
The rancher's 5 cows will require 4/1 = 4 bags of feed corn each, or 5*4 = <<5*4=20>>20 bags of feed corn in total for the month.
Therefore, the rancher needs 16+20 = <<16+20=36>>36 bags of feed corn for all of his animals.
So, the rancher will need to spend 36*10 = $<<36*10=360>>360 per year on feed corn.
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