There are some vans and motorcycles. There are 5 more motorcycles than vans. The total number of van wheels is 16 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 + 5 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 10 |
16 |
(a)
Number of vans = 1 u
Number of motorcycles = 1 u + 5
Number of van wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 5)
= 2 u + 10
Number of more van wheels than motorcycle wheels
= 4 u - (2 u + 10)
= 2 u - 10
2 u - 10 = 16
2 u = 16 + 10
2 u = 26
1 u = 26 ÷ 2 = 13
Number of motorcycles
= 1 u + 5
= 13 + 5
= 18
(b)
Total number of wheels
= 4 u + 2 u + 10
= 6 u + 10
= 6 x 13 + 10
= 78 + 10
= 88
Total number of wheels that belongs to the extra $(cars)
= 140 - 88
= 52
Number of more vans needed in order to get a total of 140 wheels
= 52 ÷ 4
= 13
Answer(s): (a) 18; (b) 13