Final answer:
To find the number of bushels of corn and oats that Mr. Mitchell should mix to obtain 180 bu of feed worth $3.10/bu, we can set up a system of equations and solve for the values of x and y. Using the equations 3.72x + 2.12y = 3.10(180) and x + y = 180, we find that Mr. Mitchell should mix 110 bushels of corn and 70 bushels of oats.
Step-by-step explanation:
To find the number of bushels of corn and oats that Mr. Mitchell should mix to obtain 180 bu of feed worth $3.10/bu, we can set up a system of equations:
Let x be the number of bushels of corn, and y be the number of bushels of oats.
We know that the total cost of the corn and oats is the product of the quantity and cost per bushel:
3.72x + 2.12y = 3.10(180)
180 bu of feed are worth $3.10/bu, so the total value of the feed is 3.10(180) = $558.
We also know that the total quantity of corn and oats is 180 bu:
x + y = 180
We can use these two equations to solve for x and y.
Multiplying the second equation by 2.12, we get:
2.12x + 2.12y = 2.12(180)
Subtracting this equation from the first equation, we eliminate the y term:
(3.72x + 2.12y) - (2.12x + 2.12y) = (3.10(180) - 2.12(180))
Simplifying, we have:
3.72x - 2.12x = 558 - 2.12(180)
1.6x = 558 - 381.6
1.6x = 176.4
x = 110
Substituting x = 110 into the second equation, we can solve for y:
110 + y = 180
y = 180 - 110
y = 70
So, Mr. Mitchell should mix 110 bushels of corn and 70 bushels of oats to obtain 180 bu of feed worth $3.10/bu.