The petrol tank of Liam's convertible was 60% empty. He went to the petrol station and topped up 12 ℓ of petrol. When he reached the bistro, the petrol tank was 70% full. Given that he used 3 ℓ of fuel to get to the bistro from the kiosk, find the capacity of the petrol tank.
|
Full |
Empty |
Total |
Before |
2x2 = 4 u |
3x2 = 6 u |
5x2 = 10 u |
Change 1 |
+ 12 |
- 12 |
|
Change 2 |
- 3 |
+ 3 |
|
After |
7x1 = 7 u |
3x1 = 3 u |
10x1 = 10 u |
60% =
60100 =
35 Empty : Total = 3 : 5
70% =
70100 =
710 Full : Total = 7 : 10
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 5 and 10 is 10.
Volume of petrol in the end
= 4 u + 12 - 3
= 4 u + 9
7 u = 4 u + 9
7 u - 4 u = 9
3 u = 9
1 u = 9 ÷ 3 = 3
Capacity of the petrol tank
= 10 u
= 10 x 3
= 30 ℓ
Answer(s): 30 ℓ