There are some cars and motorcycles. There are 8 more motorcycles than cars. The total number of car wheels is 12 more than the total number of motorcycle wheels.
- How many motorcycles are there?
- How many more cars are needed in order to get a total of 160 wheels?
| |
Cars |
Motorcycles |
More |
| Number |
1 u |
1 u + 8 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 16 |
12 |
(a)
Number of cars = 1 u
Number of motorcycles = 1 u + 8
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 8)
= 2 u + 16
Number of more car wheels than motorcycle wheels
= 4 u - (2 u + 16)
= 2 u - 16
2 u - 16 = 12
2 u = 12 + 16
2 u = 28
1 u = 28 ÷ 2 = 14
Number of motorcycles
= 1 u + 8
= 14 + 8
= 22
(b)
Total number of wheels
= 4 u + 2 u + 16
= 6 u + 16
= 6 x 14 + 16
= 84 + 16
= 100
Total number of wheels that belongs to the extra $(cars)
= 160 - 100
= 60
Number of more cars needed in order to get a total of 160 wheels
= 60 ÷ 4
= 15
Answer(s): (a) 22; (b) 15
