Archie and Justin each had the same volume of water. The water was used to pour into identical bottles. Archie filled up 11 bottles and had 2 ℓ of water left. Justin filled up 7 bottles and had 2.8 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 Justin 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 = 11 B + 2 --- (1)
Volume of water that Justin had = 7 B + 2.8 --- (2)
The volume of water that Archie and Justin have is the same.
(1) = (2)
11 B + 2 = 7 B + 2.8
11 B - 7 B = 2.8 - 2
4 B = 0.8
1 B = 0.8 ÷ 4 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 11 bottles
= 11 x 0.2
= 2.2 ℓ
Volume of water that Archie had at first
= 11 B + 2
= 11 x 0.2 + 2
= 2.2 + 2
= 4.2 ℓ
Total volume of water that Archie and Justin had at first
= 2 x 4.2
= 8.4 ℓ
Answer(s): (a) 200 mℓ; (b) 8.4 ℓ
