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Simplifying 27x + 115(x + 100) + 52(x + 200) + 19(x + 300) = 110297.79 Reorder the terms: 27x + 115(100 + x) + 52(x + 200) + 19(x + 300) = 110297.79 27x + (100 * 115 + x * 115) + 52(x + 200) + 19(x + 300) = 110297.79 27x + (11500 + 115x) + 52(x + 200) + 19(x + 300) = 110297.79 Reorder the terms: 27x + 11500 + 115x + 52(200 + x) + 19(x + 300) = 110297.79 27x + 11500 + 115x + (200 * 52 + x * 52) + 19(x + 300) = 110297.79 27x + 11500 + 115x + (10400 + 52x) + 19(x + 300) = 110297.79 Reorder the terms: 27x + 11500 + 115x + 10400 + 52x + 19(300 + x) = 110297.79 27x + 11500 + 115x + 10400 + 52x + (300 * 19 + x * 19) = 110297.79 27x + 11500 + 115x + 10400 + 52x + (5700 + 19x) = 110297.79 Reorder the terms: 11500 + 10400 + 5700 + 27x + 115x + 52x + 19x = 110297.79 Combine like terms: 11500 + 10400 = 21900 21900 + 5700 + 27x + 115x + 52x + 19x = 110297.79 Combine like terms: 21900 + 5700 = 27600 27600 + 27x + 115x + 52x + 19x = 110297.79 Combine like terms: 27x + 115x = 142x 27600 + 142x + 52x + 19x = 110297.79 Combine like terms: 142x + 52x = 194x 27600 + 194x + 19x = 110297.79 Combine like terms: 194x + 19x = 213x 27600 + 213x = 110297.79 Solving 27600 + 213x = 110297.79 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27600' to each side of the equation. 27600 + -27600 + 213x = 110297.79 + -27600 Combine like terms: 27600 + -27600 = 0 0 + 213x = 110297.79 + -27600 213x = 110297.79 + -27600 Combine like terms: 110297.79 + -27600 = 82697.79 213x = 82697.79 Divide each side by '213'. x = 388.2525352 Simplifying x = 388.2525352
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