There are some cars and motorbikes. There are 15 more motorbikes than cars. The total number of car wheels is 10 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 174 wheels?
| |
Cars |
Motorbikes |
More |
| Number |
1 u |
1 u + 15 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 30 |
10 |
(a)
Number of cars = 1 u
Number of motorbikes = 1 u + 15
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorbike wheels
= 2 x (1 u + 15)
= 2 u + 30
Number of more car wheels than motorbike wheels
= 4 u - (2 u + 30)
= 2 u - 30
2 u - 30 = 10
2 u = 10 + 30
2 u = 40
1 u = 40 ÷ 2 = 20
Number of motorbikes
= 1 u + 15
= 20 + 15
= 35
(b)
Total number of wheels
= 4 u + 2 u + 30
= 6 u + 30
= 6 x 20 + 30
= 120 + 30
= 150
Total number of wheels that belongs to the extra $(cars)
= 174 - 150
= 24
Number of more cars needed in order to get a total of 174 wheels
= 24 ÷ 4
= 6
Answer(s): (a) 35; (b) 6
