let X be number of quarts of 4% milk

let Y be number of quarts of 1% milk

The total of X and Y are 60 quarts

X + Y = 60 (*)

quarts of 4% milk and 1% milk should be mixed to yield quarts of 2% milk

<=> X(4%) + Y(1%) = (X + Y)(2%)

<=> 4X + Y = 120 (**), multiplying both sides by 100 and substituting X + Y = 60

Now, subtracting (**) to (*) to find X

(4X + y) - (X+Y) = 120 -60

3X = 60

X = 20

hence,

from (*), Y = 60 - x = 60 - 20 = 40