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Simplifying 0.05n + 0.10(n + 9) + 0.25(n + 30) = 10.00 Reorder the terms: 0.05n + 0.10(9 + n) + 0.25(n + 30) = 10.00 0.05n + (9 * 0.10 + n * 0.10) + 0.25(n + 30) = 10.00 0.05n + (0.9 + 0.10n) + 0.25(n + 30) = 10.00 Reorder the terms: 0.05n + 0.9 + 0.10n + 0.25(30 + n) = 10.00 0.05n + 0.9 + 0.10n + (30 * 0.25 + n * 0.25) = 10.00 0.05n + 0.9 + 0.10n + (7.5 + 0.25n) = 10.00 Reorder the terms: 0.9 + 7.5 + 0.05n + 0.10n + 0.25n = 10.00 Combine like terms: 0.9 + 7.5 = 8.4 8.4 + 0.05n + 0.10n + 0.25n = 10.00 Combine like terms: 0.05n + 0.10n = 0.15n 8.4 + 0.15n + 0.25n = 10.00 Combine like terms: 0.15n + 0.25n = 0.4n 8.4 + 0.4n = 10.00 Solving 8.4 + 0.4n = 10.00 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8.4' to each side of the equation. 8.4 + -8.4 + 0.4n = 10.00 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + 0.4n = 10.00 + -8.4 0.4n = 10.00 + -8.4 Combine like terms: 10.00 + -8.4 = 1.6 0.4n = 1.6 Divide each side by '0.4'. n = 4 Simplifying n = 4
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