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A worker at a farm supply company in Franklin County is mixing up a 420-kilogram batch of its special grain blend for horses, which costs $5.80 per kilogram to make. If the mixture includes oats that cost $9.40 per kilogram and feed corn that costs $3.40 per kilogram, how many kilograms of each should the worker include in the mixture?

_?__ Kilograms of oats
_?__ Kilograms of feed corn

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Answer:

168 kg oats and 252 kg corn

Step-by-step explanation:

2 equations and 2 unknowns

eq 1: x + y = 420

x is the amount of oats

y is amount of corn

eq 2: 9.4x + 3.4y = 5.8*420

solve equation 1 for x

x = 420 - y

substitute the value of x in eq 2

9.4(420-y) + 3.4y = 2436

y = 252

substitute y in eq 1

x + 252 = 420

x = 168

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