The ratio of the number of vans to the number of motorcycles is 11:15.

Question

The ratio of the number of vans to the number of motorcycles is 11:15. Each van has 4 wheels and each motorcycle has 2 wheels. If all the vans and motorcycles have a total of 592 wheels, how many wheels do all the vans have altogether?

Answer 1

Let v = the number of vans and m = the number of motorcycles.  The ratio of the number of vans to the number of motorcycles is 11:15

 

v/m = 11/15

v = (11/15)m

 

Each van has 4 wheels and each motorcycle has 2 wheels.All of the vans and motorcycles have a total of 592 wheels

 

     4v + 2m = 592

 

Substitute (11m/15) in place of v:

 

     4(11m/15) + 2m = 592

     44m/15 + 2m = 592

     44m/15 + 30m/15 = 592

     74m/15 = 592

     m = 120     There are 120 motorcycles

 

     v = (11/15)m

     v = (11/15)(120)

     v = 88        There are 88 vans

 

Check:

     4v + 2m = 592

     4*88 + 2*120 = 592

     352 + 240 = 592

     592 = 592

     Check!

Answer 2

 

 

 number of total wheels for all van = 11*4x

number of total wheel of all motor cycle =15* 2x

 

11*4x + 15 * 2x =592

 

44x +30x=592

 

74 x =592

 

x= 8

 

number of total wheels for all van = 11*4x=11*4*8=352