Albert and Michael each had the same volume of water. The water was used to pour into identical bottles. Albert filled up 18 bottles and had 3 ℓ of water left. Michael filled up 12 bottles and had 3.66 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Albert 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 Albert had = 18 B + 3 --- (1)
Volume of water that Michael had = 12 B + 3.66 --- (2)
The volume of water that Albert and Michael have is the same.
(1) = (2)
18 B + 3 = 12 B + 3.66
18 B - 12 B = 3.66 - 3
6 B = 0.66
1 B = 0.66 ÷ 6 = 0.11
1 ℓ = 1000 mℓ
0.11 ℓ = 0.11 x 1000 = 110 mℓ
(b)
Volume of 18 bottles
= 18 x 0.11
= 1.98 ℓ
Volume of water that Albert had at first
= 18 B + 3
= 18 x 0.11 + 3
= 1.98 + 3
= 4.98 ℓ
Total volume of water that Albert and Michael had at first
= 2 x 4.98
= 9.96 ℓ
Answer(s): (a) 110 mℓ; (b) 9.96 ℓ
