A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts

Choice B is correct. It’s given that the shop’s inventory starts with $\mathrm{4,500}$ paper cups and that the manager estimates that $70$ of these paper cups are used each day. Let $x$ represent the number of days in which the estimated supply of paper cups will reach $\mathrm{1,700}$. The equation $\mathrm{4,500}-70x=\mathrm{1,700}$ represents this situation. Subtracting $\mathrm{4,500}$ from both sides of this equation yields $-70x=-\mathrm{2,800}$. Dividing both sides of this equation by $-70$ yields $x=40$. Therefore, based on this estimate, the supply of paper cups will reach $\mathrm{1,700}$ in $40$ days.

Choice A is incorrect. After $20$ days, the estimated supply of paper cups would be $\mathrm{4,500}-70\left(20\right)$, or $\mathrm{3,100}$ cups, not $\mathrm{1,700}$ cups.

Choice C is incorrect. After $60$ days, the estimated supply of paper cups would be $\mathrm{4,500}-70\left(60\right)$, or $300$ cups, not $\mathrm{1,700}$ cups.

Choice D is incorrect. After $80$ days, the estimated supply of paper cups would be $\mathrm{4,500}-70\left(80\right)$, or $-\mathrm{1,100}$ cups, which isn't possible.