The petrol tank of Tommy's convertible was 50% empty. He went to the petrol station and topped up 14 ℓ of petrol. When he reached the mosque, the petrol tank was 90% full. Given that he used 6 ℓ of fuel to get to the mosque 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 |
+ 14 |
- 14 |
|
Change 2 |
- 6 |
+ 6 |
|
After |
9x1 = 9 u |
1x1 = 1 u |
10x1 = 10 u |
50% =
50100 =
12 Empty : Total = 1 : 2
90% =
90100 =
910 Full : Total = 9 : 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 + 14 - 6
= 5 u + 8
9 u = 5 u + 8
9 u - 5 u = 8
4 u = 8
1 u = 8 ÷ 4 = 2
Capacity of the petrol tank
= 10 u
= 10 x 2
= 20 ℓ
Answer(s): 20 ℓ