Elijah and Paul each had the same volume of water. The water was used to pour into identical bottles. Elijah filled up 14 bottles and had 7 ℓ of water left. Paul filled up 8 bottles and had 10 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Elijah and Paul had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Elijah had = 14 B + 7 --- (1)
Volume of water that Paul had = 8 B + 10 --- (2)
The volume of water that Elijah and Paul have is the same.
(1) = (2)
14 B + 7 = 8 B + 10
14 B - 8 B = 10 - 7
6 B = 3
1 B = 3 ÷ 6 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 14 bottles
= 14 x 0.5
= 7 ℓ
Volume of water that Elijah had at first
= 14 B + 7
= 14 x 0.5 + 7
= 7 + 7
= 14 ℓ
Total volume of water that Elijah and Paul had at first
= 2 x 14
= 28 ℓ
Answer(s): (a) 500 mℓ; (b) 28 ℓ
