[tex]c-number\ of\ cars\\v-number\ of\ vans\\\\c:v=5:2\to\dfrac{c}{v}=\dfrac{5}{2}\to c=\dfrac{5}{2}v\qquad(*)\\\\c-\dfrac{1}{3}c=v+16\to\dfrac{2}{3}c=v+16\qquad(**)\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\\dfrac{\not2}{3}\left(\dfrac{5}{\not2}v\right)=v+16\\\\\dfrac{5}{3}v=v+16\\\\1\dfrac{2}{3}v=v+16\qquad\text{subtract v from both sides}\\\\\dfrac{2}{3}v=16\qquad\text{multiply both sides by 3}\\\\2v=48\qquad\text{divide both sides by 2}\\\\\boxed{v=24}\\\\Answer:\ \boxed{24\ vans}[/tex]
