Nick and Oliver each had the same volume of water. The water was used to pour into identical bottles. Nick filled up 11 bottles and had 5 ℓ of water left. Oliver filled up 7 bottles and had 5.48 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 Oliver 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 = 11 B + 5 --- (1)
Volume of water that Oliver had = 7 B + 5.48 --- (2)
The volume of water that Nick and Oliver have is the same.
(1) = (2)
11 B + 5 = 7 B + 5.48
11 B - 7 B = 5.48 - 5
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 11 bottles
= 11 x 0.12
= 1.32 ℓ
Volume of water that Nick had at first
= 11 B + 5
= 11 x 0.12 + 5
= 1.32 + 5
= 6.32 ℓ
Total volume of water that Nick and Oliver had at first
= 2 x 6.32
= 12.64 ℓ
Answer(s): (a) 120 mℓ; (b) 12.64 ℓ
