.1a+.6(200-a)=.5(200)

Solution for .1a+.6(200-a)=.5(200) equation:

Simplifying
0.1a + 0.6(200 + -1a) = 0.5(200)
0.1a + (200 * 0.6 + -1a * 0.6) = 0.5(200)
0.1a + (120 + -0.6a) = 0.5(200)

Reorder the terms:
120 + 0.1a + -0.6a = 0.5(200)

Combine like terms: 0.1a + -0.6a = -0.5a
120 + -0.5a = 0.5(200)

Multiply 0.5 * 200
120 + -0.5a = 100

Solving
120 + -0.5a = 100

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-120' to each side of the equation.
120 + -120 + -0.5a = 100 + -120

Combine like terms: 120 + -120 = 0
0 + -0.5a = 100 + -120
-0.5a = 100 + -120

Combine like terms: 100 + -120 = -20
-0.5a = -20

Divide each side by '-0.5'.
a = 40

Simplifying
a = 40