Brandon and Howard each had the same volume of water. The water was used to pour into identical bottles. Brandon filled up 16 bottles and had 3 ℓ of water left. Howard filled up 10 bottles and had 6 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Brandon and Howard had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Brandon had = 16 B + 3 --- (1)
Volume of water that Howard had = 10 B + 6 --- (2)
The volume of water that Brandon and Howard have is the same.
(1) = (2)
16 B + 3 = 10 B + 6
16 B - 10 B = 6 - 3
6 B = 3
1 B = 3 ÷ 6 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 16 bottles
= 16 x 0.5
= 8 ℓ
Volume of water that Brandon had at first
= 16 B + 3
= 16 x 0.5 + 3
= 8 + 3
= 11 ℓ
Total volume of water that Brandon and Howard had at first
= 2 x 11
= 22 ℓ
Answer(s): (a) 500 mℓ; (b) 22 ℓ
