Luke and Neave each had the same volume of water. The water was used to pour into identical bottles. Luke filled up 14 bottles and had 6 ℓ of water left. Neave filled up 12 bottles and had 6.5 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Luke 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 Luke had = 14 B + 6 --- (1)
Volume of water that Neave had = 12 B + 6.5 --- (2)
The volume of water that Luke and Neave have is the same.
(1) = (2)
14 B + 6 = 12 B + 6.5
14 B - 12 B = 6.5 - 6
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 14 bottles
= 14 x 0.25
= 3.5 ℓ
Volume of water that Luke had at first
= 14 B + 6
= 14 x 0.25 + 6
= 3.5 + 6
= 9.5 ℓ
Total volume of water that Luke and Neave had at first
= 2 x 9.5
= 19 ℓ
Answer(s): (a) 250 mℓ; (b) 19 ℓ