Caden and Jack each had the same volume of water. The water was used to pour into identical bottles. Caden filled up 13 bottles and had 5 ℓ of water left. Jack filled up 9 bottles and had 5.48 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Caden and Jack had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Caden had = 13 B + 5 --- (1)
Volume of water that Jack had = 9 B + 5.48 --- (2)
The volume of water that Caden and Jack have is the same.
(1) = (2)
13 B + 5 = 9 B + 5.48
13 B - 9 B = 5.48 - 5
4 B = 0.48
1 B = 0.48 ÷ 4 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 13 bottles
= 13 x 0.12
= 1.56 ℓ
Volume of water that Caden had at first
= 13 B + 5
= 13 x 0.12 + 5
= 1.56 + 5
= 6.56 ℓ
Total volume of water that Caden and Jack had at first
= 2 x 6.56
= 13.12 ℓ
Answer(s): (a) 120 mℓ; (b) 13.12 ℓ
