There are some vans and bicycles. There are 5 more bicycles than vans. The total number of van wheels is 24 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 172 wheels?
|
Vans |
Bicycles |
More |
Number |
1 u |
1 u + 5 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 10 |
24 |
(a)
Number of vans = 1 u
Number of bicycles = 1 u + 5
Number of van wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 5)
= 2 u + 10
Number of more van wheels than bicycle wheels
= 4 u - (2 u + 10)
= 2 u - 10
2 u - 10 = 24
2 u = 24 + 10
2 u = 34
1 u = 34 ÷ 2 = 17
Number of bicycles
= 1 u + 5
= 17 + 5
= 22
(b)
Total number of wheels
= 4 u + 2 u + 10
= 6 u + 10
= 6 x 17 + 10
= 102 + 10
= 112
Total number of wheels that belongs to the extra $(cars)
= 172 - 112
= 60
Number of more vans needed in order to get a total of 172 wheels
= 60 ÷ 4
= 15
Answer(s): (a) 22; (b) 15