Let x be the number of vans and y the number of cars.
We are told that for every 3 vans we get 5 car. This translates to the equation
[tex]y\text{ = }\frac{5}{3}x[/tex]Note that if we replace x=3, we get y=5 which is what we are told.
Now, we have 96 vehicles in total, so
[tex]x+y\text{ = 96}[/tex]Now, we replace the value of y with what we found in the first equation, so
[tex]x\text{ + }\frac{5}{3}x\text{ = 96 = }\frac{8}{3}x[/tex]If we multiply by 3 on both sides, we get
[tex]8x\text{ = 96}\cdot3\text{ = 288 }[/tex]If we now divide by 8 we get
[tex]x\text{ = }\frac{288}{8}\text{ = 36}[/tex]Since x+y = 96 and x = 36, then we must have y = 60.
So, there are 36 vans and 60 cars
