# Warwick’s Workings, part II

This post will mainly make sense to Warwick – if you aren’t Warwick and you need some context, see the Twitter thread starting with this twitter post. $u_{cost} \text{ is the number of units at cost price}$ $p_{cost} \text{ is the unit cost price}$ $u_{current} \text{ is the number of units at the current price}$ $p_{current} \text{ is the current unit price}$ $p_{target} \text{ is the target unit price}$ $\frac {u_{cost} p_{cost} + u_{current} p_{current}} {u_{cost} + u_{current}} = p_{target}$ $\Rightarrow u_{cost} p_{cost} + u_{current} p_{current} = p_{target} (u_{cost} + u_{current})$ $\Rightarrow u_{cost} p_{cost} + u_{current} p_{current} = p_{target} u_{cost} + u_{current} p_{target}$ $\Rightarrow u_{current} p_{current} - u_{current} p_{target} = p_{target} u_{cost} - u_{cost} p_{cost}$ $\Rightarrow u_{current} (p_{current} - p_{target}) = u_{cost} (p_{target} - p_{cost})$ $\text{The formula you$ $u_{current} = \frac {u_{cost} (p_{target} - p_{cost})} {(p_{current} - p_{target})}$ $\text{Proving it works using the given figures:}$ $u_{current} = \frac {336 * (14 - 18.23)} {(13 - 14)}$ $\Rightarrow u_{current} = \frac {(-1421.28)} {(-1)}$ $\Rightarrow u_{current} = 1421.28$