, 2024

Of the $4050$ trucks sold, $32\%$ were white or $\dfrac{32}{100}\cdot4050=1296$ were white. Solution 1: Of the $4050$ trucks sold, $24\%$ were grey or $\dfrac{24}{100}\cdot4050=972$ were grey. Since $\dfrac14$ of the grey trucks sold were electric, then $\dfrac14\cdot972=243$ trucks sold were both grey and electric. Solution 2: Since $24\%$ of the trucks sold were grey, and $\dfrac14$ of those were electric, then $\dfrac{24}{100}\cdot\dfrac14=\dfrac{6}{100}$ (or $6\%$) were both grey and electric. Thus, of the $4050$ trucks sold, $\dfrac{6}{100}\cdot4050=243$ were both grey and electric. Solution 1: Of the $4050$ trucks sold, $44\%$ were black or $\dfrac{44}{100}\cdot4050=1782$ were black. Thus, the total number of black trucks, sold and unsold, was $1782+k$, and the total number of trucks, sold and unsold, was $4050+k$. Since $46\%$ of all trucks, sold and unsold, were black, then $\dfrac{1782+k}{4050+k}=\dfrac{46}{100}$. Solving, we get $$\begin{align*} \dfrac{1782+k}{4050+k}&=\dfrac{46}{100} \\ \dfrac{1782+k}{4050+k}&=\dfrac{23}{50} \\ 50(1782+k)&=23(4050+k) \\ 89\,100+50k&=93\,150+23k \\ 27k&=4050\\ k&=150\end{align*}$$ and so there were $150$ unsold trucks, all of which were black. Solution 2: Of the $4050$ trucks sold, $44\%$ were black and so $100\%-44\%=56\%$ were not black. Therefore, $\dfrac{56}{100}\cdot4050=2268$ trucks sold were not black. Since all unsold trucks were black, then there were $2268$ trucks, sold and unsold, that were not black. Since $46\%$ of all trucks, sold and unsold, were black, then $100\%-46\%=54\%$ of all trucks, sold and unsold, were not black. The total number of trucks, sold and unsold, was $4050+k$ and $54\%$ of these trucks were not black, thus $\dfrac{2268}{4050+k}=\dfrac{54}{100}$. Solving, we get $$\begin{align*} \dfrac{2268}{4050+k}&=\dfrac{54}{100} \\ \dfrac{2268}{4050+k}&=\dfrac{27}{50} \\ 50(2268)&=27(4050+k) \\ 113\,400&=109\,350+27k \\ 4050&=27k\\ k&=150\end{align*}$$ and so there were $150$ unsold trucks, all of which were
black.