There are some vans and scooters. There are 11 more scooters than vans. The total number of van wheels is 16 more than the total number of scooter wheels.

1. How many scooters are there?
2. How many more vans are needed in order to get a total of 172 wheels?

	Vans	Scooters	More
Number	1 u	1 u + 11
Value	4	2
Total value	4 u	2 u + 22	16

(a)
Number of vans = 1 u
Number of scooters = 1 u + 11

Number of van wheels 
= 4 x 1 u
= 4 u

Number of scooter wheels
= 2 x (1 u + 11)
= 2 u + 22

Number of more van wheels than scooter wheels
= 4 u - (2 u + 22)
= 2 u - 22

2 u - 22 = 16
2 u = 16 + 22
2 u = 38

1 u = 38 ÷ 2 = 19

Number of scooters
= 1 u + 11
= 19 + 11
= 30

(b)
Total number of wheels
= 4 u + 2 u + 22
= 6 u + 22
= 6 x 19 + 22
= 114 + 22
= 136

Total number of wheels that belongs to the extra $(cars)
= 172 - 136
= 36

Number of more vans needed in order to get a total of 172 wheels
= 36 ÷ 4
= 9

Answer(s): (a) 30; (b) 9