The petrol tank of Brandon's van was 50% empty. He went to the petrol kiosk and topped up 11 ℓ of petrol. When he reached the park, the petrol tank was 75% full. Given that he used 6 ℓ of fuel to get to the park 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 |
+ 11 |
- 11 |
|
| Change 2 |
- 6 |
+ 6 |
|
| 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 + 11 - 6
= 2 u + 5
3 u = 2 u + 5
3 u - 2 u = 5
1 u = 5
Capacity of the petrol tank
= 4 u
= 4 x 5
= 20 ℓ
Answer(s): 20 ℓ
