There are some cars and bicycles. There are 4 more bicycles than cars. The total number of car wheels is 24 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 140 wheels?
|
Cars |
Bicycles |
More |
Number |
1 u |
1 u + 4 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 8 |
24 |
(a)
Number of cars = 1 u
Number of bicycles = 1 u + 4
Number of car wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 4)
= 2 u + 8
Number of more car wheels than bicycle wheels
= 4 u - (2 u + 8)
= 2 u - 8
2 u - 8 = 24
2 u = 24 + 8
2 u = 32
1 u = 32 ÷ 2 = 16
Number of bicycles
= 1 u + 4
= 16 + 4
= 20
(b)
Total number of wheels
= 4 u + 2 u + 8
= 6 u + 8
= 6 x 16 + 8
= 96 + 8
= 104
Total number of wheels that belongs to the extra $(cars)
= 140 - 104
= 36
Number of more cars needed in order to get a total of 140 wheels
= 36 ÷ 4
= 9
Answer(s): (a) 20; (b) 9