There are some vans and motorcycles. There are 6 more motorcycles than vans. The total number of van wheels is 20 more than the total number of motorcycle wheels.
- How many motorcycles are there?
- How many more vans are needed in order to get a total of 140 wheels?
| |
Vans |
Motorcycles |
More |
| Number |
1 u |
1 u + 6 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 12 |
20 |
(a)
Number of vans = 1 u
Number of motorcycles = 1 u + 6
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 6)
= 2 u + 12
Number of more van wheels than motorcycle wheels
= 4 u - (2 u + 12)
= 2 u - 12
2 u - 12 = 20
2 u = 20 + 12
2 u = 32
1 u = 32 ÷ 2 = 16
Number of motorcycles
= 1 u + 6
= 16 + 6
= 22
(b)
Total number of wheels
= 4 u + 2 u + 12
= 6 u + 12
= 6 x 16 + 12
= 96 + 12
= 108
Total number of wheels that belongs to the extra $(cars)
= 140 - 108
= 32
Number of more vans needed in order to get a total of 140 wheels
= 32 ÷ 4
= 8
Answer(s): (a) 22; (b) 8
