There are some vans and motorcycles. There are 12 more motorcycles than vans. The total number of van wheels is 14 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 174 wheels?
| |
Vans |
Motorcycles |
More |
| Number |
1 u |
1 u + 12 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 24 |
14 |
(a)
Number of vans = 1 u
Number of motorcycles = 1 u + 12
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 12)
= 2 u + 24
Number of more van wheels than motorcycle wheels
= 4 u - (2 u + 24)
= 2 u - 24
2 u - 24 = 14
2 u = 14 + 24
2 u = 38
1 u = 38 ÷ 2 = 19
Number of motorcycles
= 1 u + 12
= 19 + 12
= 31
(b)
Total number of wheels
= 4 u + 2 u + 24
= 6 u + 24
= 6 x 19 + 24
= 114 + 24
= 138
Total number of wheels that belongs to the extra $(cars)
= 174 - 138
= 36
Number of more vans needed in order to get a total of 174 wheels
= 36 ÷ 4
= 9
Answer(s): (a) 31; (b) 9
