Billy and Cole each had the same volume of water. The water was used to pour into identical bottles. Billy filled up 16 bottles and had 6 ℓ of water left. Cole filled up 14 bottles and had 6.24 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Billy and Cole had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Billy had = 16 B + 6 --- (1)
Volume of water that Cole had = 14 B + 6.24 --- (2)
The volume of water that Billy and Cole have is the same.
(1) = (2)
16 B + 6 = 14 B + 6.24
16 B - 14 B = 6.24 - 6
2 B = 0.24
1 B = 0.24 ÷ 2 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 16 bottles
= 16 x 0.12
= 1.92 ℓ
Volume of water that Billy had at first
= 16 B + 6
= 16 x 0.12 + 6
= 1.92 + 6
= 7.92 ℓ
Total volume of water that Billy and Cole had at first
= 2 x 7.92
= 15.84 ℓ
Answer(s): (a) 120 mℓ; (b) 15.84 ℓ
