100(0.05x+0.02(90))=100(0.03(x+90))

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Solution for 100(0.05x+0.02(90))=100(0.03(x+90)) equation:


Simplifying
100(0.05x + 0.02(90)) = 100(0.03(x + 90))

Multiply 0.02 * 90
100(0.05x + 1.8) = 100(0.03(x + 90))

Reorder the terms:
100(1.8 + 0.05x) = 100(0.03(x + 90))
(1.8 * 100 + 0.05x * 100) = 100(0.03(x + 90))
(180 + 5x) = 100(0.03(x + 90))

Reorder the terms:
180 + 5x = 100(0.03(90 + x))
180 + 5x = 100((90 * 0.03 + x * 0.03))
180 + 5x = 100((2.7 + 0.03x))
180 + 5x = (2.7 * 100 + 0.03x * 100)
180 + 5x = (270 + 3x)

Solving
180 + 5x = 270 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
180 + 5x + -3x = 270 + 3x + -3x

Combine like terms: 5x + -3x = 2x
180 + 2x = 270 + 3x + -3x

Combine like terms: 3x + -3x = 0
180 + 2x = 270 + 0
180 + 2x = 270

Add '-180' to each side of the equation.
180 + -180 + 2x = 270 + -180

Combine like terms: 180 + -180 = 0
0 + 2x = 270 + -180
2x = 270 + -180

Combine like terms: 270 + -180 = 90
2x = 90

Divide each side by '2'.
x = 45

Simplifying
x = 45

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