There are some vans and motorbikes. There are 3 more motorbikes than vans. The total number of van wheels is 8 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 68 wheels?
| |
Vans |
Motorbikes |
More |
| Number |
1 u |
1 u + 3 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 6 |
8 |
(a)
Number of vans = 1 u
Number of motorbikes = 1 u + 3
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 3)
= 2 u + 6
Number of more van wheels than motorbike wheels
= 4 u - (2 u + 6)
= 2 u - 6
2 u - 6 = 8
2 u = 8 + 6
2 u = 14
1 u = 14 ÷ 2 = 7
Number of motorbikes
= 1 u + 3
= 7 + 3
= 10
(b)
Total number of wheels
= 4 u + 2 u + 6
= 6 u + 6
= 6 x 7 + 6
= 42 + 6
= 48
Total number of wheels that belongs to the extra $(cars)
= 68 - 48
= 20
Number of more vans needed in order to get a total of 68 wheels
= 20 ÷ 4
= 5
Answer(s): (a) 10; (b) 5
