Bryan and Mark each had the same volume of water. The water was used to pour into identical bottles. Bryan filled up 18 bottles and had 5 ℓ of water left. Mark filled up 14 bottles and had 5.44 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 Mark 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 = 18 B + 5 --- (1)
Volume of water that Mark had = 14 B + 5.44 --- (2)
The volume of water that Bryan and Mark have is the same.
(1) = (2)
18 B + 5 = 14 B + 5.44
18 B - 14 B = 5.44 - 5
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 18 bottles
= 18 x 0.11
= 1.98 ℓ
Volume of water that Bryan had at first
= 18 B + 5
= 18 x 0.11 + 5
= 1.98 + 5
= 6.98 ℓ
Total volume of water that Bryan and Mark had at first
= 2 x 6.98
= 13.96 ℓ
Answer(s): (a) 110 mℓ; (b) 13.96 ℓ
