2024 AMC 8 Problem 19

Jordan owns 15 pairs of sneakers. Three fifths of the pairs are red and the rest are white. Two thirds of the pairs are high-top and the rest are low-top. The red high-top sneakers make up a fraction of the collection. What is the least possible value of this fraction?

\textbf{(A)} 0 \qquad \textbf{(B)} \dfrac{1}{5} \qquad \textbf{(C)} \dfrac{4}{15} \qquad \textbf{(D)} \dfrac{1}{3} \qquad \textbf{(E)} \dfrac{2}{5}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.