Tom and Valen each had the same volume of water. The water was used to pour into identical bottles. Tom filled up 15 bottles and had 6 ℓ of water left. Valen filled up 13 bottles and had 6.28 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 Valen 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 = 15 B + 6 --- (1)
Volume of water that Valen had = 13 B + 6.28 --- (2)
The volume of water that Tom and Valen have is the same.
(1) = (2)
15 B + 6 = 13 B + 6.28
15 B - 13 B = 6.28 - 6
2 B = 0.28
1 B = 0.28 ÷ 2 = 0.14
1 ℓ = 1000 mℓ
0.14 ℓ = 0.14 x 1000 = 140 mℓ
(b)
Volume of 15 bottles
= 15 x 0.14
= 2.1 ℓ
Volume of water that Tom had at first
= 15 B + 6
= 15 x 0.14 + 6
= 2.1 + 6
= 8.1 ℓ
Total volume of water that Tom and Valen had at first
= 2 x 8.1
= 16.2 ℓ
Answer(s): (a) 140 mℓ; (b) 16.2 ℓ
