George and Valen each had the same volume of water. The water was used to pour into identical bottles. George filled up 17 bottles and had 2 ℓ of water left. Valen filled up 13 bottles and had 2.56 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 Valen 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 = 17 B + 2 --- (1)
Volume of water that Valen had = 13 B + 2.56 --- (2)
The volume of water that George and Valen have is the same.
(1) = (2)
17 B + 2 = 13 B + 2.56
17 B - 13 B = 2.56 - 2
4 B = 0.56
1 B = 0.56 ÷ 4 = 0.14
1 ℓ = 1000 mℓ
0.14 ℓ = 0.14 x 1000 = 140 mℓ
(b)
Volume of 17 bottles
= 17 x 0.14
= 2.38 ℓ
Volume of water that George had at first
= 17 B + 2
= 17 x 0.14 + 2
= 2.38 + 2
= 4.38 ℓ
Total volume of water that George and Valen had at first
= 2 x 4.38
= 8.76 ℓ
Answer(s): (a) 140 mℓ; (b) 8.76 ℓ
