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Simplifying 100(80 + -1t) = 50(t + -20) (80 * 100 + -1t * 100) = 50(t + -20) (8000 + -100t) = 50(t + -20) Reorder the terms: 8000 + -100t = 50(-20 + t) 8000 + -100t = (-20 * 50 + t * 50) 8000 + -100t = (-1000 + 50t) Solving 8000 + -100t = -1000 + 50t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-50t' to each side of the equation. 8000 + -100t + -50t = -1000 + 50t + -50t Combine like terms: -100t + -50t = -150t 8000 + -150t = -1000 + 50t + -50t Combine like terms: 50t + -50t = 0 8000 + -150t = -1000 + 0 8000 + -150t = -1000 Add '-8000' to each side of the equation. 8000 + -8000 + -150t = -1000 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -150t = -1000 + -8000 -150t = -1000 + -8000 Combine like terms: -1000 + -8000 = -9000 -150t = -9000 Divide each side by '-150'. t = 60 Simplifying t = 60
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