The petrol tank of Ethan's van was 50% empty. He went to the petrol station and topped up 11 ℓ of petrol. When he reached the library, the petrol tank was 80% full. Given that he used 2 ℓ of fuel to get to the library from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
1x5 =
5 u |
1x5 =
5 u |
2x5 =
10 u |
| Change 1 |
+ 11 |
- 11 |
|
| Change 2 |
- 2 |
+ 2 |
|
| After |
4x2 =
8 u |
1x2 =
2 u |
5x2 =
10 u |
50% =
50100 =
12 Empty : Total = 1 : 2
80% =
80100 =
45 Full : Total = 4 : 5
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 2 and 5 is 10.
Volume of petrol in the end
= 5 u + 11 - 2
= 5 u + 9
8 u = 5 u + 9
8 u - 5 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
