There are some vans and motorbikes. There are 8 more motorbikes than vans. The total number of van wheels is 22 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 158 wheels?
| |
Vans |
Motorbikes |
More |
| Number |
1 u |
1 u + 8 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 16 |
22 |
(a)
Number of vans = 1 u
Number of motorbikes = 1 u + 8
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 8)
= 2 u + 16
Number of more van wheels than motorbike wheels
= 4 u - (2 u + 16)
= 2 u - 16
2 u - 16 = 22
2 u = 22 + 16
2 u = 38
1 u = 38 ÷ 2 = 19
Number of motorbikes
= 1 u + 8
= 19 + 8
= 27
(b)
Total number of wheels
= 4 u + 2 u + 16
= 6 u + 16
= 6 x 19 + 16
= 114 + 16
= 130
Total number of wheels that belongs to the extra $(cars)
= 158 - 130
= 28
Number of more vans needed in order to get a total of 158 wheels
= 28 ÷ 4
= 7
Answer(s): (a) 27; (b) 7
