There are some cars and bicycles. There are 15 more bicycles than cars. The total number of car wheels is 8 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 176 wheels?
| |
Cars |
Bicycles |
More |
| Number |
1 u |
1 u + 15 |
|
| Value |
4 |
2 |
|
| Total value |
4 u |
2 u + 30 |
8 |
(a)
Number of cars = 1 u
Number of bicycles = 1 u + 15
Number of car wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 15)
= 2 u + 30
Number of more car wheels than bicycle wheels
= 4 u - (2 u + 30)
= 2 u - 30
2 u - 30 = 8
2 u = 8 + 30
2 u = 38
1 u = 38 ÷ 2 = 19
Number of bicycles
= 1 u + 15
= 19 + 15
= 34
(b)
Total number of wheels
= 4 u + 2 u + 30
= 6 u + 30
= 6 x 19 + 30
= 114 + 30
= 144
Total number of wheels that belongs to the extra $(cars)
= 176 - 144
= 32
Number of more cars needed in order to get a total of 176 wheels
= 32 ÷ 4
= 8
Answer(s): (a) 34; (b) 8
