There are some vans and motorbikes. There are 2 more motorbikes than vans. The total number of van wheels is 16 more than the total number of motorbike wheels.
- How many motorbikes are there?
- How many more vans are needed in order to get a total of 92 wheels?
|
Vans |
Motorbikes |
More |
Number |
1 u |
1 u + 2 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 4 |
16 |
(a)
Number of vans = 1 u
Number of motorbikes = 1 u + 2
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 2)
= 2 u + 4
Number of more van wheels than motorbike wheels
= 4 u - (2 u + 4)
= 2 u - 4
2 u - 4 = 16
2 u = 16 + 4
2 u = 20
1 u = 20 ÷ 2 = 10
Number of motorbikes
= 1 u + 2
= 10 + 2
= 12
(b)
Total number of wheels
= 4 u + 2 u + 4
= 6 u + 4
= 6 x 10 + 4
= 60 + 4
= 64
Total number of wheels that belongs to the extra $(cars)
= 92 - 64
= 28
Number of more vans needed in order to get a total of 92 wheels
= 28 ÷ 4
= 7
Answer(s): (a) 12; (b) 7