Daniel and Vincent each had the same volume of water. The water was used to pour into identical bottles. Daniel filled up 13 bottles and had 2 ℓ of water left. Vincent filled up 11 bottles and had 2.44 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Daniel and Vincent had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Daniel had = 13 B + 2 --- (1)
Volume of water that Vincent had = 11 B + 2.44 --- (2)
The volume of water that Daniel and Vincent have is the same.
(1) = (2)
13 B + 2 = 11 B + 2.44
13 B - 11 B = 2.44 - 2
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 13 bottles
= 13 x 0.22
= 2.86 ℓ
Volume of water that Daniel had at first
= 13 B + 2
= 13 x 0.22 + 2
= 2.86 + 2
= 4.86 ℓ
Total volume of water that Daniel and Vincent had at first
= 2 x 4.86
= 9.72 ℓ
Answer(s): (a) 220 mℓ; (b) 9.72 ℓ
