Oscar and Fabian each had the same volume of water. The water was used to pour into identical bottles. Oscar filled up 11 bottles and had 2 ℓ of water left. Fabian filled up 9 bottles and had 2.3 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Oscar and Fabian had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Oscar had = 11 B + 2 --- (1)
Volume of water that Fabian had = 9 B + 2.3 --- (2)
The volume of water that Oscar and Fabian have is the same.
(1) = (2)
11 B + 2 = 9 B + 2.3
11 B - 9 B = 2.3 - 2
2 B = 0.3
1 B = 0.3 ÷ 2 = 0.15
1 ℓ = 1000 mℓ
0.15 ℓ = 0.15 x 1000 = 150 mℓ
(b)
Volume of 11 bottles
= 11 x 0.15
= 1.65 ℓ
Volume of water that Oscar had at first
= 11 B + 2
= 11 x 0.15 + 2
= 1.65 + 2
= 3.65 ℓ
Total volume of water that Oscar and Fabian had at first
= 2 x 3.65
= 7.3 ℓ
Answer(s): (a) 150 mℓ; (b) 7.3 ℓ
