Billy and Asher each had the same volume of water. The water was used to pour into identical bottles. Billy filled up 11 bottles and had 2 ℓ of water left. Asher filled up 9 bottles and had 3 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Billy and Asher had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Billy had = 11 B + 2 --- (1)
Volume of water that Asher had = 9 B + 3 --- (2)
The volume of water that Billy and Asher have is the same.
(1) = (2)
11 B + 2 = 9 B + 3
11 B - 9 B = 3 - 2
2 B = 1
1 B = 1 ÷ 2 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 11 bottles
= 11 x 0.5
= 5.5 ℓ
Volume of water that Billy had at first
= 11 B + 2
= 11 x 0.5 + 2
= 5.5 + 2
= 7.5 ℓ
Total volume of water that Billy and Asher had at first
= 2 x 7.5
= 15 ℓ
Answer(s): (a) 500 mℓ; (b) 15 ℓ
