There are some cars and bicycles. There are 5 more bicycles than cars. The total number of car wheels is 20 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 144 wheels?
|
Cars |
Bicycles |
More |
Number |
1 u |
1 u + 5 |
|
Value |
4 |
2 |
|
Total value |
4 u |
2 u + 10 |
20 |
(a)
Number of cars = 1 u
Number of bicycles = 1 u + 5
Number of car wheels
= 4 x 1 u
= 4 u
Number of bicycle wheels
= 2 x (1 u + 5)
= 2 u + 10
Number of more car wheels than bicycle wheels
= 4 u - (2 u + 10)
= 2 u - 10
2 u - 10 = 20
2 u = 20 + 10
2 u = 30
1 u = 30 ÷ 2 = 15
Number of bicycles
= 1 u + 5
= 15 + 5
= 20
(b)
Total number of wheels
= 4 u + 2 u + 10
= 6 u + 10
= 6 x 15 + 10
= 90 + 10
= 100
Total number of wheels that belongs to the extra $(cars)
= 144 - 100
= 44
Number of more cars needed in order to get a total of 144 wheels
= 44 ÷ 4
= 11
Answer(s): (a) 20; (b) 11