Bryan and Gabriel each had the same volume of water. The water was used to pour into identical bottles. Bryan filled up 13 bottles and had 7 ℓ of water left. Gabriel filled up 11 bottles and had 7.28 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 Gabriel 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 = 13 B + 7 --- (1)
Volume of water that Gabriel had = 11 B + 7.28 --- (2)
The volume of water that Bryan and Gabriel have is the same.
(1) = (2)
13 B + 7 = 11 B + 7.28
13 B - 11 B = 7.28 - 7
2 B = 0.28
1 B = 0.28 ÷ 2 = 0.14
1 ℓ = 1000 mℓ
0.14 ℓ = 0.14 x 1000 = 140 mℓ
(b)
Volume of 13 bottles
= 13 x 0.14
= 1.82 ℓ
Volume of water that Bryan had at first
= 13 B + 7
= 13 x 0.14 + 7
= 1.82 + 7
= 8.82 ℓ
Total volume of water that Bryan and Gabriel had at first
= 2 x 8.82
= 17.64 ℓ
Answer(s): (a) 140 mℓ; (b) 17.64 ℓ
