Fred and Valen each had the same volume of water. The water was used to pour into identical bottles. Fred filled up 13 bottles and had 4 ℓ of water left. Valen filled up 9 bottles and had 5.6 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Fred 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 Fred had = 13 B + 4 --- (1)
Volume of water that Valen had = 9 B + 5.6 --- (2)
The volume of water that Fred and Valen have is the same.
(1) = (2)
13 B + 4 = 9 B + 5.6
13 B - 9 B = 5.6 - 4
4 B = 1.6
1 B = 1.6 ÷ 4 = 0.4
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
(b)
Volume of 13 bottles
= 13 x 0.4
= 5.2 ℓ
Volume of water that Fred had at first
= 13 B + 4
= 13 x 0.4 + 4
= 5.2 + 4
= 9.2 ℓ
Total volume of water that Fred and Valen had at first
= 2 x 9.2
= 18.4 ℓ
Answer(s): (a) 400 mℓ; (b) 18.4 ℓ
