There are some vans and bicycles. There are 2 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 118 wheels?
|
Vans |
Bicycles |
More |
Number |
1 u |
1 u + 2 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 4 |
22 |
(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 = 22
2 u = 22 + 4
2 u = 26
1 u = 26 ÷ 2 = 13
Number of bicycles
= 1 u + 2
= 13 + 2
= 15
(b)
Total number of wheels
= 4 u + 2 u + 4
= 6 u + 4
= 6 x 13 + 4
= 78 + 4
= 82
Total number of wheels that belongs to the extra $(cars)
= 118 - 82
= 36
Number of more vans needed in order to get a total of 118 wheels
= 36 ÷ 4
= 9
Answer(s): (a) 15; (b) 9