There are some vans and motorbikes. There are 12 more motorbikes than vans. The total number of van wheels is 10 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 150 wheels?
| |
Vans |
Motorbikes |
More |
| Number |
1 u |
1 u + 12 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 24 |
10 |
(a)
Number of vans = 1 u
Number of motorbikes = 1 u + 12
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 12)
= 2 u + 24
Number of more van wheels than motorbike wheels
= 4 u - (2 u + 24)
= 2 u - 24
2 u - 24 = 10
2 u = 10 + 24
2 u = 34
1 u = 34 ÷ 2 = 17
Number of motorbikes
= 1 u + 12
= 17 + 12
= 29
(b)
Total number of wheels
= 4 u + 2 u + 24
= 6 u + 24
= 6 x 17 + 24
= 102 + 24
= 126
Total number of wheels that belongs to the extra $(cars)
= 150 - 126
= 24
Number of more vans needed in order to get a total of 150 wheels
= 24 ÷ 4
= 6
Answer(s): (a) 29; (b) 6
