There are some vans and motorbikes. There are 11 more motorbikes than vans. The total number of van wheels is 14 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 170 wheels?
| |
Vans |
Motorbikes |
More |
| Number |
1 u |
1 u + 11 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 22 |
14 |
(a)
Number of vans = 1 u
Number of motorbikes = 1 u + 11
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 11)
= 2 u + 22
Number of more van wheels than motorbike wheels
= 4 u - (2 u + 22)
= 2 u - 22
2 u - 22 = 14
2 u = 14 + 22
2 u = 36
1 u = 36 ÷ 2 = 18
Number of motorbikes
= 1 u + 11
= 18 + 11
= 29
(b)
Total number of wheels
= 4 u + 2 u + 22
= 6 u + 22
= 6 x 18 + 22
= 108 + 22
= 130
Total number of wheels that belongs to the extra $(cars)
= 170 - 130
= 40
Number of more vans needed in order to get a total of 170 wheels
= 40 ÷ 4
= 10
Answer(s): (a) 29; (b) 10
