Daniel and Jeremy each had the same volume of water. The water was used to pour into identical bottles. Daniel filled up 18 bottles and had 2 ℓ of water left. Jeremy filled up 12 bottles and had 5 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Daniel and Jeremy had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Daniel had = 18 B + 2 --- (1)
Volume of water that Jeremy had = 12 B + 5 --- (2)
The volume of water that Daniel and Jeremy have is the same.
(1) = (2)
18 B + 2 = 12 B + 5
18 B - 12 B = 5 - 2
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 18 bottles
= 18 x 0.5
= 9 ℓ
Volume of water that Daniel had at first
= 18 B + 2
= 18 x 0.5 + 2
= 9 + 2
= 11 ℓ
Total volume of water that Daniel and Jeremy had at first
= 2 x 11
= 22 ℓ
Answer(s): (a) 500 mℓ; (b) 22 ℓ
