Charlie and Xavier each had the same volume of water. The water was used to pour into identical bottles. Charlie filled up 12 bottles and had 2 ℓ of water left. Xavier filled up 10 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 Charlie and Xavier had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Charlie had = 12 B + 2 --- (1)
Volume of water that Xavier had = 10 B + 3 --- (2)
The volume of water that Charlie and Xavier have is the same.
(1) = (2)
12 B + 2 = 10 B + 3
12 B - 10 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 12 bottles
= 12 x 0.5
= 6 ℓ
Volume of water that Charlie had at first
= 12 B + 2
= 12 x 0.5 + 2
= 6 + 2
= 8 ℓ
Total volume of water that Charlie and Xavier had at first
= 2 x 8
= 16 ℓ
Answer(s): (a) 500 mℓ; (b) 16 ℓ
