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Simplifying 13a + 14b + 15c + 16d = 1000 Solving 13a + 14b + 15c + 16d = 1000 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-14b' to each side of the equation. 13a + 14b + 15c + -14b + 16d = 1000 + -14b Reorder the terms: 13a + 14b + -14b + 15c + 16d = 1000 + -14b Combine like terms: 14b + -14b = 0 13a + 0 + 15c + 16d = 1000 + -14b 13a + 15c + 16d = 1000 + -14b Add '-15c' to each side of the equation. 13a + 15c + -15c + 16d = 1000 + -14b + -15c Combine like terms: 15c + -15c = 0 13a + 0 + 16d = 1000 + -14b + -15c 13a + 16d = 1000 + -14b + -15c Add '-16d' to each side of the equation. 13a + 16d + -16d = 1000 + -14b + -15c + -16d Combine like terms: 16d + -16d = 0 13a + 0 = 1000 + -14b + -15c + -16d 13a = 1000 + -14b + -15c + -16d Divide each side by '13'. a = 76.92307692 + -1.076923077b + -1.153846154c + -1.230769231d Simplifying a = 76.92307692 + -1.076923077b + -1.153846154c + -1.230769231d
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