There are some vans and bicycles. There are 3 more bicycles than vans. The total number of van wheels is 22 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 134 wheels?
| |
Vans |
Bicycles |
More |
| Number |
1 u |
1 u + 3 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 6 |
22 |
(a)
Number of vans = 1 u
Number of bicycles = 1 u + 3
Number of van wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 3)
= 2 u + 6
Number of more van wheels than bicycle wheels
= 4 u - (2 u + 6)
= 2 u - 6
2 u - 6 = 22
2 u = 22 + 6
2 u = 28
1 u = 28 ÷ 2 = 14
Number of bicycles
= 1 u + 3
= 14 + 3
= 17
(b)
Total number of wheels
= 4 u + 2 u + 6
= 6 u + 6
= 6 x 14 + 6
= 84 + 6
= 90
Total number of wheels that belongs to the extra $(cars)
= 134 - 90
= 44
Number of more vans needed in order to get a total of 134 wheels
= 44 ÷ 4
= 11
Answer(s): (a) 17; (b) 11
