There are some cars and motorcycles. There are 7 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 130 wheels?
|
Cars |
Motorcycles |
More |
Number |
1 u |
1 u + 7 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 14 |
14 |
(a)
Number of cars = 1 u
Number of motorcycles = 1 u + 7
Number of car wheels
= 4 x 1 u
= 4 u
Number of motorcycle wheels
= 2 x (1 u + 7)
= 2 u + 14
Number of more car wheels than motorcycle wheels
= 4 u - (2 u + 14)
= 2 u - 14
2 u - 14 = 14
2 u = 14 + 14
2 u = 28
1 u = 28 ÷ 2 = 14
Number of motorcycles
= 1 u + 7
= 14 + 7
= 21
(b)
Total number of wheels
= 4 u + 2 u + 14
= 6 u + 14
= 6 x 14 + 14
= 84 + 14
= 98
Total number of wheels that belongs to the extra $(cars)
= 130 - 98
= 32
Number of more cars needed in order to get a total of 130 wheels
= 32 ÷ 4
= 8
Answer(s): (a) 21; (b) 8