There are some vans and bicycles. There are 4 more bicycles than vans. The total number of van wheels is 30 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 150 wheels?
|
Vans |
Bicycles |
More |
Number |
1 u |
1 u + 4 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 8 |
30 |
(a)
Number of vans = 1 u
Number of bicycles = 1 u + 4
Number of van wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 4)
= 2 u + 8
Number of more van wheels than bicycle wheels
= 4 u - (2 u + 8)
= 2 u - 8
2 u - 8 = 30
2 u = 30 + 8
2 u = 38
1 u = 38 ÷ 2 = 19
Number of bicycles
= 1 u + 4
= 19 + 4
= 23
(b)
Total number of wheels
= 4 u + 2 u + 8
= 6 u + 8
= 6 x 19 + 8
= 114 + 8
= 122
Total number of wheels that belongs to the extra $(cars)
= 150 - 122
= 28
Number of more vans needed in order to get a total of 150 wheels
= 28 ÷ 4
= 7
Answer(s): (a) 23; (b) 7