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Simplifying 0.5x + 1y + 2z + 2.5p = 100 Reorder the terms: 2.5p + 0.5x + 1y + 2z = 100 Solving 2.5p + 0.5x + 1y + 2z = 100 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5x' to each side of the equation. 2.5p + 0.5x + 1y + -0.5x + 2z = 100 + -0.5x Reorder the terms: 2.5p + 0.5x + -0.5x + 1y + 2z = 100 + -0.5x Combine like terms: 0.5x + -0.5x = 0.0 2.5p + 0.0 + 1y + 2z = 100 + -0.5x 2.5p + 1y + 2z = 100 + -0.5x Add '-1y' to each side of the equation. 2.5p + 1y + -1y + 2z = 100 + -0.5x + -1y Combine like terms: 1y + -1y = 0 2.5p + 0 + 2z = 100 + -0.5x + -1y 2.5p + 2z = 100 + -0.5x + -1y Add '-2z' to each side of the equation. 2.5p + 2z + -2z = 100 + -0.5x + -1y + -2z Combine like terms: 2z + -2z = 0 2.5p + 0 = 100 + -0.5x + -1y + -2z 2.5p = 100 + -0.5x + -1y + -2z Divide each side by '2.5'. p = 40 + -0.2x + -0.4y + -0.8z Simplifying p = 40 + -0.2x + -0.4y + -0.8z
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