The petrol tank of Elijah's sports car was 50% empty. He went to the petrol station and topped up 26 ℓ of petrol. When he reached the market, the petrol tank was 90% full. Given that he used 10 ℓ of fuel to get to the market 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 |
+ 26 |
- 26 |
|
| Change 2 |
- 10 |
+ 10 |
|
| 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 + 26 - 10
= 5 u + 16
9 u = 5 u + 16
9 u - 5 u = 16
4 u = 16
1 u = 16 ÷ 4 = 4
Capacity of the petrol tank
= 10 u
= 10 x 4
= 40 ℓ
Answer(s): 40 ℓ
