There are some vans and bicycles. There are 2 more bicycles than vans. The total number of van wheels is 32 more than the total number of bicycle wheels.
- How many bicycles are there?
- How many more vans are needed in order to get a total of 136 wheels?
| |
Vans |
Bicycles |
More |
| Number |
1 u |
1 u + 2 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 4 |
32 |
(a)
Number of vans = 1 u
Number of bicycles = 1 u + 2
Number of van wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 2)
= 2 u + 4
Number of more van wheels than bicycle wheels
= 4 u - (2 u + 4)
= 2 u - 4
2 u - 4 = 32
2 u = 32 + 4
2 u = 36
1 u = 36 ÷ 2 = 18
Number of bicycles
= 1 u + 2
= 18 + 2
= 20
(b)
Total number of wheels
= 4 u + 2 u + 4
= 6 u + 4
= 6 x 18 + 4
= 108 + 4
= 112
Total number of wheels that belongs to the extra $(cars)
= 136 - 112
= 24
Number of more vans needed in order to get a total of 136 wheels
= 24 ÷ 4
= 6
Answer(s): (a) 20; (b) 6
