content of fat in x gallons of 1% grade milk => 0.01*x
content of fat in y gallons of 2% grade milk => 0.02*y
content of fat in z gallons of 3% grade milk => 0.03*z

total content of fat in the resulting mixture of 1.5% grade milk = grade*volume = 0.015 * (x+y+z)

so, our equation is:
0.015 (x+y+z) = 0.01*x + 0.02*y + 0.03*z
multiplying everything by 100, we get
1.5(x+y+z) = x + 2y + 3z
or 1.5x + 1.5y + 1.5z = x + 2y + 3z
or 0.5x = 0.5y + 1.5z
or x = y + 3z

Fat in milk is x*1%, y*2% and z*3%, respectively.

So we have the equation: x*1% + y*2% + z*3% =(x + y +z)*1.5%

Simplify the equation, we can obtain that x = y + 3 z