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I am trying to work through understanding this but I do not know how they got to the solution at the bottom (b*). Any help?

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Just algebra. Plug their $s^*$ into the first of the 2 equations $b\cdot B_1...$ then move things around so that $b$ is alone on the left hand side.

Like so: $$b \cdot B_1 + \Big( {{C^u_1-C^d_1}\over{S^u_1-S^d_1}} \Big) S^u_1 = C^u_1,$$ then $$b \cdot B_1 = C^u_1 - \Big( {{C^u_1-C^d_1}\over{S^u_1-S^d_1}} \Big) S^u_1,$$ then $$b \cdot B_1 = C^u_1 \Big( {{S^u_1-S^d_1}\over{S^u_1-S^d_1}} \Big) - \Big( {{C^u_1-C^d_1}\over{S^u_1-S^d_1}} \Big) S^u_1,$$ then $$b \cdot B_1 = {{C^d_1 S^u_1-C^u_1 S^d_1}\over{S^u_1-S^d_1}}$$ Etc.

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  • $\begingroup$ Sorry, I still don't understand what you mean. When I try to move them around I don't get the answer at the bottom. $\endgroup$ Dec 27, 2021 at 19:57
  • $\begingroup$ Thanks so much for your help! $\endgroup$ Dec 27, 2021 at 20:13

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