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Simplifying 0 = 1000 + -10r + 0.8y + -0.8(200 + -0.2y) + 3000 + -40r + 3000 + 600 + -0.14y 0 = 1000 + -10r + 0.8y + (200 * -0.8 + -0.2y * -0.8) + 3000 + -40r + 3000 + 600 + -0.14y 0 = 1000 + -10r + 0.8y + (-160 + 0.16y) + 3000 + -40r + 3000 + 600 + -0.14y Reorder the terms: 0 = 1000 + -160 + 3000 + 3000 + 600 + -10r + -40r + 0.8y + 0.16y + -0.14y Combine like terms: 1000 + -160 = 840 0 = 840 + 3000 + 3000 + 600 + -10r + -40r + 0.8y + 0.16y + -0.14y Combine like terms: 840 + 3000 = 3840 0 = 3840 + 3000 + 600 + -10r + -40r + 0.8y + 0.16y + -0.14y Combine like terms: 3840 + 3000 = 6840 0 = 6840 + 600 + -10r + -40r + 0.8y + 0.16y + -0.14y Combine like terms: 6840 + 600 = 7440 0 = 7440 + -10r + -40r + 0.8y + 0.16y + -0.14y Combine like terms: -10r + -40r = -50r 0 = 7440 + -50r + 0.8y + 0.16y + -0.14y Combine like terms: 0.8y + 0.16y = 0.96y 0 = 7440 + -50r + 0.96y + -0.14y Combine like terms: 0.96y + -0.14y = 0.82y 0 = 7440 + -50r + 0.82y Solving 0 = 7440 + -50r + 0.82y Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '50r' to each side of the equation. 0 + 50r = 7440 + -50r + 50r + 0.82y Remove the zero: 50r = 7440 + -50r + 50r + 0.82y Combine like terms: -50r + 50r = 0 50r = 7440 + 0 + 0.82y 50r = 7440 + 0.82y Divide each side by '50'. r = 148.8 + 0.0164y Simplifying r = 148.8 + 0.0164y
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