.85t+.15(10-t)=.51(10)

Solution for .85t+.15(10-t)=.51(10) equation:

Simplifying
0.85t + 0.15(10 + -1t) = 0.51(10)
0.85t + (10 * 0.15 + -1t * 0.15) = 0.51(10)
0.85t + (1.5 + -0.15t) = 0.51(10)

Reorder the terms:
1.5 + 0.85t + -0.15t = 0.51(10)

Combine like terms: 0.85t + -0.15t = 0.7t
1.5 + 0.7t = 0.51(10)

Multiply 0.51 * 10
1.5 + 0.7t = 5.1

Solving
1.5 + 0.7t = 5.1

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + 0.7t = 5.1 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.7t = 5.1 + -1.5
0.7t = 5.1 + -1.5

Combine like terms: 5.1 + -1.5 = 3.6
0.7t = 3.6

Divide each side by '0.7'.
t = 5.142857143

Simplifying
t = 5.142857143