There are some cars and bicycles. There are 3 more bicycles than cars. The total number of car wheels is 34 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 174 wheels?
| |
Cars |
Bicycles |
More |
| Number |
1 u |
1 u + 3 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 6 |
34 |
(a)
Number of cars = 1 u
Number of bicycles = 1 u + 3
Number of car wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 3)
= 2 u + 6
Number of more car wheels than bicycle wheels
= 4 u - (2 u + 6)
= 2 u - 6
2 u - 6 = 34
2 u = 34 + 6
2 u = 40
1 u = 40 ÷ 2 = 20
Number of bicycles
= 1 u + 3
= 20 + 3
= 23
(b)
Total number of wheels
= 4 u + 2 u + 6
= 6 u + 6
= 6 x 20 + 6
= 120 + 6
= 126
Total number of wheels that belongs to the extra $(cars)
= 174 - 126
= 48
Number of more cars needed in order to get a total of 174 wheels
= 48 ÷ 4
= 12
Answer(s): (a) 23; (b) 12
