Archie and Oscar each had the same volume of water. The water was used to pour into identical bottles. Archie filled up 15 bottles and had 6 ℓ of water left. Oscar filled up 13 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 Archie and Oscar had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Archie had = 15 B + 6 --- (1)
Volume of water that Oscar had = 13 B + 6.5 --- (2)
The volume of water that Archie and Oscar have is the same.
(1) = (2)
15 B + 6 = 13 B + 6.5
15 B - 13 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 15 bottles
= 15 x 0.25
= 3.75 ℓ
Volume of water that Archie had at first
= 15 B + 6
= 15 x 0.25 + 6
= 3.75 + 6
= 9.75 ℓ
Total volume of water that Archie and Oscar had at first
= 2 x 9.75
= 19.5 ℓ
Answer(s): (a) 250 mℓ; (b) 19.5 ℓ