There are some vans and bicycles. There are 10 more bicycles than vans. The total number of van wheels is 10 more than the total number of bicycle wheels.

1. How many bicycles are there?
2. How many more vans are needed in order to get a total of 170 wheels?

	Vans	Bicycles	More
Number	1 u	1 u + 10
Value	4	2
Total value	4 u	2 u + 20	10

(a)
Number of vans = 1 u
Number of bicycles = 1 u + 10

Number of van wheels 
= 4 x 1 u
= 4 u

Number of bicycle wheels
= 2 x (1 u + 10)
= 2 u + 20

Number of more van wheels than bicycle wheels
= 4 u - (2 u + 20)
= 2 u - 20

2 u - 20 = 10
2 u = 10 + 20
2 u = 30

1 u = 30 ÷ 2 = 15

Number of bicycles
= 1 u + 10
= 15 + 10
= 25

(b)
Total number of wheels
= 4 u + 2 u + 20
= 6 u + 20
= 6 x 15 + 20
= 90 + 20
= 110

Total number of wheels that belongs to the extra $(cars)
= 170 - 110
= 60

Number of more vans needed in order to get a total of 170 wheels
= 60 ÷ 4
= 15

Answer(s): (a) 25; (b) 15