The petrol tank of Howard's van was 70% empty. He went to the petrol kiosk and topped up 35 ℓ of petrol. When he reached the bistro, the petrol tank was 95% full. Given that he used 9 ℓ of fuel to get to the bistro 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 |
+ 35 |
- 35 |
|
| Change 2 |
- 9 |
+ 9 |
|
| 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 + 35 - 9
= 6 u + 26
19 u = 6 u + 26
19 u - 6 u = 26
13 u = 26
1 u = 26 ÷ 13 = 2
Capacity of the petrol tank
= 20 u
= 20 x 2
= 40 ℓ
Answer(s): 40 ℓ
