Valen and Owen each had the same volume of water. The water was used to pour into identical bottles. Valen filled up 16 bottles and had 5 ℓ of water left. Owen filled up 14 bottles and had 5.44 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Valen and Owen had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Valen had = 16 B + 5 --- (1)
Volume of water that Owen had = 14 B + 5.44 --- (2)
The volume of water that Valen and Owen have is the same.
(1) = (2)
16 B + 5 = 14 B + 5.44
16 B - 14 B = 5.44 - 5
2 B = 0.44
1 B = 0.44 ÷ 2 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 16 bottles
= 16 x 0.22
= 3.52 ℓ
Volume of water that Valen had at first
= 16 B + 5
= 16 x 0.22 + 5
= 3.52 + 5
= 8.52 ℓ
Total volume of water that Valen and Owen had at first
= 2 x 8.52
= 17.04 ℓ
Answer(s): (a) 220 mℓ; (b) 17.04 ℓ
