The petrol tank of Howard's sports car was 70% empty. He went to the petrol station and topped up 46 ℓ of petrol. When he reached the bakery, the petrol tank was 95% full. Given that he used 7 ℓ of fuel to get to the bakery from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
3x2 =
6 u |
7x2 =
14 u |
10x2 =
20 u |
| Change 1 |
+ 46 |
- 46 |
|
| Change 2 |
- 7 |
+ 7 |
|
| After |
19x1 =
19 u |
1x1 =
1 u |
20x1 =
20 u |
70% =
70100 =
710 Empty : Total = 7 : 10
95% =
95100 =
1920 Full : Total = 19 : 20
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 10 and 20 is 20.
Volume of petrol in the end
= 6 u + 46 - 7
= 6 u + 39
19 u = 6 u + 39
19 u - 6 u = 39
13 u = 39
1 u = 39 ÷ 13 = 3
Capacity of the petrol tank
= 20 u
= 20 x 3
= 60 ℓ
Answer(s): 60 ℓ
