There are some cars and motorcycles. There are 3 more motorcycles than cars. The total number of car wheels is 14 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 102 wheels?
|
Cars |
Motorcycles |
More |
Number |
1 u |
1 u + 3 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 6 |
14 |
(a)
Number of cars = 1 u
Number of motorcycles = 1 u + 3
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 3)
= 2 u + 6
Number of more car wheels than motorcycle wheels
= 4 u - (2 u + 6)
= 2 u - 6
2 u - 6 = 14
2 u = 14 + 6
2 u = 20
1 u = 20 ÷ 2 = 10
Number of motorcycles
= 1 u + 3
= 10 + 3
= 13
(b)
Total number of wheels
= 4 u + 2 u + 6
= 6 u + 6
= 6 x 10 + 6
= 60 + 6
= 66
Total number of wheels that belongs to the extra $(cars)
= 102 - 66
= 36
Number of more cars needed in order to get a total of 102 wheels
= 36 ÷ 4
= 9
Answer(s): (a) 13; (b) 9