Jack and Neave each had the same volume of water. The water was used to pour into identical bottles. Jack filled up 12 bottles and had 5 ℓ of water left. Neave filled up 10 bottles and had 5.24 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Jack and Neave had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Jack had = 12 B + 5 --- (1)
Volume of water that Neave had = 10 B + 5.24 --- (2)
The volume of water that Jack and Neave have is the same.
(1) = (2)
12 B + 5 = 10 B + 5.24
12 B - 10 B = 5.24 - 5
2 B = 0.24
1 B = 0.24 ÷ 2 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 12 bottles
= 12 x 0.12
= 1.44 ℓ
Volume of water that Jack had at first
= 12 B + 5
= 12 x 0.12 + 5
= 1.44 + 5
= 6.44 ℓ
Total volume of water that Jack and Neave had at first
= 2 x 6.44
= 12.88 ℓ
Answer(s): (a) 120 mℓ; (b) 12.88 ℓ
