The petrol tank of Oliver's van was 50% empty. He went to the petrol station and topped up 16 ℓ of petrol. When he reached the bank, the petrol tank was 75% full. Given that he used 9 ℓ of fuel to get to the bank from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
1x2 =
2 u |
1x2 =
2 u |
2x2 =
4 u |
| Change 1 |
+ 16 |
- 16 |
|
| Change 2 |
- 9 |
+ 9 |
|
| After |
3x1 =
3 u |
1x1 =
1 u |
4x1 =
4 u |
50% =
50100 =
12 Empty : Total = 1 : 2
75% =
75100 =
34 Full : Total = 3 : 4
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 2 and 4 is 4.
Volume of petrol in the end
= 2 u + 16 - 9
= 2 u + 7
3 u = 2 u + 7
3 u - 2 u = 7
1 u = 7
Capacity of the petrol tank
= 4 u
= 4 x 7
= 28 ℓ
Answer(s): 28 ℓ
