George and Asher each had the same volume of water. The water was used to pour into identical bottles. George filled up 20 bottles and had 4 ℓ of water left. Asher filled up 14 bottles and had 5.2 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 Asher 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 = 20 B + 4 --- (1)
Volume of water that Asher had = 14 B + 5.2 --- (2)
The volume of water that George and Asher have is the same.
(1) = (2)
20 B + 4 = 14 B + 5.2
20 B - 14 B = 5.2 - 4
6 B = 1.2
1 B = 1.2 ÷ 6 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 20 bottles
= 20 x 0.2
= 4 ℓ
Volume of water that George had at first
= 20 B + 4
= 20 x 0.2 + 4
= 4 + 4
= 8 ℓ
Total volume of water that George and Asher had at first
= 2 x 8
= 16 ℓ
Answer(s): (a) 200 mℓ; (b) 16 ℓ
