George and Michael each had the same volume of water. The water was used to pour into identical bottles. George filled up 12 bottles and had 7 ℓ of water left. Michael filled up 10 bottles and had 7.44 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water George and Michael had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that George had = 12 B + 7 --- (1)
Volume of water that Michael had = 10 B + 7.44 --- (2)
The volume of water that George and Michael have is the same.
(1) = (2)
12 B + 7 = 10 B + 7.44
12 B - 10 B = 7.44 - 7
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 12 bottles
= 12 x 0.22
= 2.64 ℓ
Volume of water that George had at first
= 12 B + 7
= 12 x 0.22 + 7
= 2.64 + 7
= 9.64 ℓ
Total volume of water that George and Michael had at first
= 2 x 9.64
= 19.28 ℓ
Answer(s): (a) 220 mℓ; (b) 19.28 ℓ
