Tom and Simon each had the same volume of water. The water was used to pour into identical bottles. Tom filled up 16 bottles and had 5 ℓ of water left. Simon filled up 14 bottles and had 5.4 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Tom and Simon had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Tom had = 16 B + 5 --- (1)
Volume of water that Simon had = 14 B + 5.4 --- (2)
The volume of water that Tom and Simon have is the same.
(1) = (2)
16 B + 5 = 14 B + 5.4
16 B - 14 B = 5.4 - 5
2 B = 0.4
1 B = 0.4 ÷ 2 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 16 bottles
= 16 x 0.2
= 3.2 ℓ
Volume of water that Tom had at first
= 16 B + 5
= 16 x 0.2 + 5
= 3.2 + 5
= 8.2 ℓ
Total volume of water that Tom and Simon had at first
= 2 x 8.2
= 16.4 ℓ
Answer(s): (a) 200 mℓ; (b) 16.4 ℓ
