Luke and Fabian each had the same volume of water. The water was used to pour into identical bottles. Luke filled up 12 bottles and had 4 ℓ of water left. Fabian filled up 8 bottles and had 4.44 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Luke and Fabian had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Luke had = 12 B + 4 --- (1)
Volume of water that Fabian had = 8 B + 4.44 --- (2)
The volume of water that Luke and Fabian have is the same.
(1) = (2)
12 B + 4 = 8 B + 4.44
12 B - 8 B = 4.44 - 4
4 B = 0.44
1 B = 0.44 ÷ 4 = 0.11
1 ℓ = 1000 mℓ
0.11 ℓ = 0.11 x 1000 = 110 mℓ
(b)
Volume of 12 bottles
= 12 x 0.11
= 1.32 ℓ
Volume of water that Luke had at first
= 12 B + 4
= 12 x 0.11 + 4
= 1.32 + 4
= 5.32 ℓ
Total volume of water that Luke and Fabian had at first
= 2 x 5.32
= 10.64 ℓ
Answer(s): (a) 110 mℓ; (b) 10.64 ℓ
