Howard and Sam each had the same volume of water. The water was used to pour into identical bottles. Howard filled up 9 bottles and had 6 ℓ of water left. Sam filled up 7 bottles and had 6.8 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 Sam 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 = 9 B + 6 --- (1)
Volume of water that Sam had = 7 B + 6.8 --- (2)
The volume of water that Howard and Sam have is the same.
(1) = (2)
9 B + 6 = 7 B + 6.8
9 B - 7 B = 6.8 - 6
2 B = 0.8
1 B = 0.8 ÷ 2 = 0.4
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
(b)
Volume of 9 bottles
= 9 x 0.4
= 3.6 ℓ
Volume of water that Howard had at first
= 9 B + 6
= 9 x 0.4 + 6
= 3.6 + 6
= 9.6 ℓ
Total volume of water that Howard and Sam had at first
= 2 x 9.6
= 19.2 ℓ
Answer(s): (a) 400 mℓ; (b) 19.2 ℓ
