Bryan and Bobby each had the same volume of water. The water was used to pour into identical bottles. Bryan filled up 14 bottles and had 2 ℓ of water left. Bobby filled up 12 bottles and had 2.4 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Bryan and Bobby had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Bryan had = 14 B + 2 --- (1)
Volume of water that Bobby had = 12 B + 2.4 --- (2)
The volume of water that Bryan and Bobby have is the same.
(1) = (2)
14 B + 2 = 12 B + 2.4
14 B - 12 B = 2.4 - 2
2 B = 0.4
1 B = 0.4 ÷ 2 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 14 bottles
= 14 x 0.2
= 2.8 ℓ
Volume of water that Bryan had at first
= 14 B + 2
= 14 x 0.2 + 2
= 2.8 + 2
= 4.8 ℓ
Total volume of water that Bryan and Bobby had at first
= 2 x 4.8
= 9.6 ℓ
Answer(s): (a) 200 mℓ; (b) 9.6 ℓ
