Archie and Michael each had the same volume of water. The water was used to pour into identical bottles. Archie filled up 14 bottles and had 7 ℓ of water left. Michael filled up 12 bottles and had 7.3 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Archie 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 Archie had = 14 B + 7 --- (1)
Volume of water that Michael had = 12 B + 7.3 --- (2)
The volume of water that Archie and Michael have is the same.
(1) = (2)
14 B + 7 = 12 B + 7.3
14 B - 12 B = 7.3 - 7
2 B = 0.3
1 B = 0.3 ÷ 2 = 0.15
1 ℓ = 1000 mℓ
0.15 ℓ = 0.15 x 1000 = 150 mℓ
(b)
Volume of 14 bottles
= 14 x 0.15
= 2.1 ℓ
Volume of water that Archie had at first
= 14 B + 7
= 14 x 0.15 + 7
= 2.1 + 7
= 9.1 ℓ
Total volume of water that Archie and Michael had at first
= 2 x 9.1
= 18.2 ℓ
Answer(s): (a) 150 mℓ; (b) 18.2 ℓ
