Howard and Ethan each had the same volume of water. The water was used to pour into identical bottles. Howard filled up 11 bottles and had 8 ℓ of water left. Ethan filled up 7 bottles and had 8.88 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Howard and Ethan had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Howard had = 11 B + 8 --- (1)
Volume of water that Ethan had = 7 B + 8.88 --- (2)
The volume of water that Howard and Ethan have is the same.
(1) = (2)
11 B + 8 = 7 B + 8.88
11 B - 7 B = 8.88 - 8
4 B = 0.88
1 B = 0.88 ÷ 4 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 11 bottles
= 11 x 0.22
= 2.42 ℓ
Volume of water that Howard had at first
= 11 B + 8
= 11 x 0.22 + 8
= 2.42 + 8
= 10.42 ℓ
Total volume of water that Howard and Ethan had at first
= 2 x 10.42
= 20.84 ℓ
Answer(s): (a) 220 mℓ; (b) 20.84 ℓ
