Ben and Archie each had the same volume of water. The water was used to pour into identical bottles. Ben filled up 11 bottles and had 5 ℓ of water left. Archie filled up 7 bottles and had 7 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Ben and Archie had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Ben had = 11 B + 5 --- (1)
Volume of water that Archie had = 7 B + 7 --- (2)
The volume of water that Ben and Archie have is the same.
(1) = (2)
11 B + 5 = 7 B + 7
11 B - 7 B = 7 - 5
4 B = 2
1 B = 2 ÷ 4 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 11 bottles
= 11 x 0.5
= 5.5 ℓ
Volume of water that Ben had at first
= 11 B + 5
= 11 x 0.5 + 5
= 5.5 + 5
= 10.5 ℓ
Total volume of water that Ben and Archie had at first
= 2 x 10.5
= 21 ℓ
Answer(s): (a) 500 mℓ; (b) 21 ℓ
