let

x = quarts of 5% butterfat milk

y = quarts of 2% butterfat milk

we mix x an y to get 30 quarts of 3% butterfat milk thus

x + y = 30

the 5% fat in x + the 2% fat in y = the 3% fat in 30 quarts

0.05x + 0.02y = 0.03*30

by solving the system of equations

x + y = 30

0.05x + 0.02y = 0.03*30

we find

x = 10 quarts

y = 20 quarts

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10 quarts of 5% butterfat milk and 20 quarts of 2% butterfat mild should be mixed to yield 30 quarts of 3% butterfat milk.