The designer spends $2121 and $3 each for hat and he can sell it for $13.50 each.
If there are x number of hats, it will cost him (2121 + 3x) and he can gain 13.50x
The break even is when the cost and sales are equal.
Equating both expressions :
![\begin{gathered} 2121+3x=13.50x \\ 2121=13.50x-3x \\ 2121=10.50x \\ x=(2121)/(10.50)=202 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/yxlb7dbht0z53bpxjv2s8jck3qgweuutes.png)
The answer is 202 hats