Nick and Ryan each had the same volume of water. The water was used to pour into identical bottles. Nick filled up 12 bottles and had 6 ℓ of water left. Ryan filled up 8 bottles and had 6.48 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Nick and Ryan had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Nick had = 12 B + 6 --- (1)
Volume of water that Ryan had = 8 B + 6.48 --- (2)
The volume of water that Nick and Ryan have is the same.
(1) = (2)
12 B + 6 = 8 B + 6.48
12 B - 8 B = 6.48 - 6
4 B = 0.48
1 B = 0.48 ÷ 4 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 12 bottles
= 12 x 0.12
= 1.44 ℓ
Volume of water that Nick had at first
= 12 B + 6
= 12 x 0.12 + 6
= 1.44 + 6
= 7.44 ℓ
Total volume of water that Nick and Ryan had at first
= 2 x 7.44
= 14.88 ℓ
Answer(s): (a) 120 mℓ; (b) 14.88 ℓ
