There are some cars and bicycles. There are 6 more bicycles than cars. The total number of car wheels is 12 more than the total number of bicycle wheels.
- How many bicycles are there?
- How many more cars are needed in order to get a total of 128 wheels?
|
Cars |
Bicycles |
More |
Number |
1 u |
1 u + 6 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 12 |
12 |
(a)
Number of cars = 1 u
Number of bicycles = 1 u + 6
Number of car wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 6)
= 2 u + 12
Number of more car wheels than bicycle wheels
= 4 u - (2 u + 12)
= 2 u - 12
2 u - 12 = 12
2 u = 12 + 12
2 u = 24
1 u = 24 ÷ 2 = 12
Number of bicycles
= 1 u + 6
= 12 + 6
= 18
(b)
Total number of wheels
= 4 u + 2 u + 12
= 6 u + 12
= 6 x 12 + 12
= 72 + 12
= 84
Total number of wheels that belongs to the extra $(cars)
= 128 - 84
= 44
Number of more cars needed in order to get a total of 128 wheels
= 44 ÷ 4
= 11
Answer(s): (a) 18; (b) 11