Japheth and Daniel each had the same volume of water. The water was used to pour into identical bottles. Japheth filled up 16 bottles and had 5 ℓ of water left. Daniel filled up 14 bottles and had 5.5 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Japheth and Daniel had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Japheth had = 16 B + 5 --- (1)
Volume of water that Daniel had = 14 B + 5.5 --- (2)
The volume of water that Japheth and Daniel have is the same.
(1) = (2)
16 B + 5 = 14 B + 5.5
16 B - 14 B = 5.5 - 5
2 B = 0.5
1 B = 0.5 ÷ 2 = 0.25
1 ℓ = 1000 mℓ
0.25 ℓ = 0.25 x 1000 = 250 mℓ
(b)
Volume of 16 bottles
= 16 x 0.25
= 4 ℓ
Volume of water that Japheth had at first
= 16 B + 5
= 16 x 0.25 + 5
= 4 + 5
= 9 ℓ
Total volume of water that Japheth and Daniel had at first
= 2 x 9
= 18 ℓ
Answer(s): (a) 250 mℓ; (b) 18 ℓ