The petrol tank of Luke's bus was 50% empty. He went to the petrol station and topped up 28 ℓ of petrol. When he reached the grocery store, the petrol tank was 85% full. Given that he used 7 ℓ of fuel to get to the grocery store from the kiosk, find the capacity of the petrol tank.
|
Full |
Empty |
Total |
Before |
1x10 = 10 u |
1x10 = 10 u |
2x10 = 20 u |
Change 1 |
+ 28 |
- 28 |
|
Change 2 |
- 7 |
+ 7 |
|
After |
17x1 = 17 u |
3x1 = 3 u |
20x1 = 20 u |
50% =
50100 =
12 Empty : Total = 1 : 2
85% =
85100 =
1720 Full : Total = 17 : 20
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 2 and 20 is 20.
Volume of petrol in the end
= 10 u + 28 - 7
= 10 u + 21
17 u = 10 u + 21
17 u - 10 u = 21
7 u = 21
1 u = 21 ÷ 7 = 3
Capacity of the petrol tank
= 20 u
= 20 x 3
= 60 ℓ
Answer(s): 60 ℓ