John and Pierre each had the same volume of water. The water was used to pour into identical bottles. John filled up 12 bottles and had 5 ℓ of water left. Pierre filled up 8 bottles and had 5.88 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water John and Pierre had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that John had = 12 B + 5 --- (1)
Volume of water that Pierre had = 8 B + 5.88 --- (2)
The volume of water that John and Pierre have is the same.
(1) = (2)
12 B + 5 = 8 B + 5.88
12 B - 8 B = 5.88 - 5
4 B = 0.88
1 B = 0.88 ÷ 4 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 12 bottles
= 12 x 0.22
= 2.64 ℓ
Volume of water that John had at first
= 12 B + 5
= 12 x 0.22 + 5
= 2.64 + 5
= 7.64 ℓ
Total volume of water that John and Pierre had at first
= 2 x 7.64
= 15.28 ℓ
Answer(s): (a) 220 mℓ; (b) 15.28 ℓ
