Tom and Justin each had the same volume of water. The water was used to pour into identical bottles. Tom filled up 12 bottles and had 3 ℓ of water left. Justin filled up 10 bottles and had 3.44 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 Justin 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 = 12 B + 3 --- (1)
Volume of water that Justin had = 10 B + 3.44 --- (2)
The volume of water that Tom and Justin have is the same.
(1) = (2)
12 B + 3 = 10 B + 3.44
12 B - 10 B = 3.44 - 3
2 B = 0.44
1 B = 0.44 ÷ 2 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 12 bottles
= 12 x 0.22
= 2.64 ℓ
Volume of water that Tom had at first
= 12 B + 3
= 12 x 0.22 + 3
= 2.64 + 3
= 5.64 ℓ
Total volume of water that Tom and Justin had at first
= 2 x 5.64
= 11.28 ℓ
Answer(s): (a) 220 mℓ; (b) 11.28 ℓ
