An airport shuttle company owns cars that have a maximum capacity of 3 passengers and vans that have a maximum capacity of 8 passengers . their 12 vehicles have a combination maximum capacity of 61 passengers. write and solve a system of equations to determine how many vans the company owns

The Total number of car is 7 and The Total number of van is 5 .

Step-by-step explanation:

Given as :

The maximum capacity of car = 3 passengers

The maximum capacity of van = 8 passengers

Total number of vehicles = c + v = 12 vehicles

The maximum capacity of vehicles combination = 61 passengers

Let The Total number of car = c

Let The Total number of van = v

Now, According to question

c + v = 12            .........A

3 c + 8 v = 61            ............B

Now, Solving eq A and B

I.e (3 c + 8 v) - 3 × (c + v) = 61 - (3 × 12)

Or, (3 c - 3 c) + (8 v - 3 v) = 61 - 36

Or, 0 + 5 v = 25

∴ v =

i.e v = 5

So,The Total number of van = v = 5

Now Put the value of v into eq A

∵ c + v = 12    

So, c + 5 = 12

∴ c = 12 - 5

i.e c = 7

So,The Total number of car = c = 7

Hence,The Total number of car is 7 and The Total number of van is 5 . Answer