The petrol tank of Carl's car was 50% empty. He went to the petrol station and topped up 15 ℓ of petrol. When he reached the church, the petrol tank was 70% full. Given that he used 9 ℓ of fuel to get to the church 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 |
+ 15 |
- 15 |
|
| Change 2 |
- 9 |
+ 9 |
|
| After |
7x1 =
7 u |
3x1 =
3 u |
10x1 =
10 u |
50% =
50100 =
12 Empty : Total = 1 : 2
70% =
70100 =
710 Full : Total = 7 : 10
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 2 and 10 is 10.
Volume of petrol in the end
= 5 u + 15 - 9
= 5 u + 6
7 u = 5 u + 6
7 u - 5 u = 6
2 u = 6
1 u = 6 ÷ 2 = 3
Capacity of the petrol tank
= 10 u
= 10 x 3
= 30 ℓ
Answer(s): 30 ℓ
