Y=200+0.8(Y-100)+200+0.1Y+100+100-100-0.15Y

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Solution for Y=200+0.8(Y-100)+200+0.1Y+100+100-100-0.15Y equation: 


Simplifying
Y = 200 + 0.8(Y + -100) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y

Reorder the terms:
Y = 200 + 0.8(-100 + Y) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y
Y = 200 + (-100 * 0.8 + Y * 0.8) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y
Y = 200 + (-80 + 0.8Y) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y

Reorder the terms:
Y = 200 + -80 + 200 + 100 + 100 + -100 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 200 + -80 = 120
Y = 120 + 200 + 100 + 100 + -100 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 120 + 200 = 320
Y = 320 + 100 + 100 + -100 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 320 + 100 = 420
Y = 420 + 100 + -100 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 420 + 100 = 520
Y = 520 + -100 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 520 + -100 = 420
Y = 420 + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 0.8Y + 0.1Y = 0.9Y
Y = 420 + 0.9Y + -0.15Y

Combine like terms: 0.9Y + -0.15Y = 0.75Y
Y = 420 + 0.75Y

Solving
Y = 420 + 0.75Y

Solving for variable 'Y'.

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

Add '-0.75Y' to each side of the equation.
Y + -0.75Y = 420 + 0.75Y + -0.75Y

Combine like terms: Y + -0.75Y = 0.25Y
0.25Y = 420 + 0.75Y + -0.75Y

Combine like terms: 0.75Y + -0.75Y = 0.00
0.25Y = 420 + 0.00
0.25Y = 420

Divide each side by '0.25'.
Y = 1680

Simplifying
Y = 1680

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