Owen and Seth each had the same volume of water. The water was used to pour into identical bottles. Owen filled up 16 bottles and had 8 ℓ of water left. Seth filled up 10 bottles and had 11 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Owen and Seth had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Owen had = 16 B + 8 --- (1)
Volume of water that Seth had = 10 B + 11 --- (2)
The volume of water that Owen and Seth have is the same.
(1) = (2)
16 B + 8 = 10 B + 11
16 B - 10 B = 11 - 8
6 B = 3
1 B = 3 ÷ 6 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 16 bottles
= 16 x 0.5
= 8 ℓ
Volume of water that Owen had at first
= 16 B + 8
= 16 x 0.5 + 8
= 8 + 8
= 16 ℓ
Total volume of water that Owen and Seth had at first
= 2 x 16
= 32 ℓ
Answer(s): (a) 500 mℓ; (b) 32 ℓ
