There are some cars and motorcycles. There are 9 more motorcycles than cars. The total number of car wheels is 20 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 164 wheels?
| |
Cars |
Motorcycles |
More |
| Number |
1 u |
1 u + 9 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 18 |
20 |
(a)
Number of cars = 1 u
Number of motorcycles = 1 u + 9
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 9)
= 2 u + 18
Number of more car wheels than motorcycle wheels
= 4 u - (2 u + 18)
= 2 u - 18
2 u - 18 = 20
2 u = 20 + 18
2 u = 38
1 u = 38 ÷ 2 = 19
Number of motorcycles
= 1 u + 9
= 19 + 9
= 28
(b)
Total number of wheels
= 4 u + 2 u + 18
= 6 u + 18
= 6 x 19 + 18
= 114 + 18
= 132
Total number of wheels that belongs to the extra $(cars)
= 164 - 132
= 32
Number of more cars needed in order to get a total of 164 wheels
= 32 ÷ 4
= 8
Answer(s): (a) 28; (b) 8
