There are some cars and motorbikes. There are 5 more motorbikes than cars. The total number of car wheels is 24 more than the total number of motorbike wheels.
- How many motorbikes are there?
- How many more cars are needed in order to get a total of 172 wheels?
| |
Cars |
Motorbikes |
More |
| Number |
1 u |
1 u + 5 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 10 |
24 |
(a)
Number of cars = 1 u
Number of motorbikes = 1 u + 5
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 5)
= 2 u + 10
Number of more car wheels than motorbike 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 motorbikes
= 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 cars needed in order to get a total of 172 wheels
= 60 ÷ 4
= 15
Answer(s): (a) 22; (b) 15
