Valen and Howard each had the same volume of water. The water was used to pour into identical bottles. Valen filled up 13 bottles and had 2 ℓ of water left. Howard filled up 7 bottles and had 3.5 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Valen and Howard had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Valen had = 13 B + 2 --- (1)
Volume of water that Howard had = 7 B + 3.5 --- (2)
The volume of water that Valen and Howard have is the same.
(1) = (2)
13 B + 2 = 7 B + 3.5
13 B - 7 B = 3.5 - 2
6 B = 1.5
1 B = 1.5 ÷ 6 = 0.25
1 ℓ = 1000 mℓ
0.25 ℓ = 0.25 x 1000 = 250 mℓ
(b)
Volume of 13 bottles
= 13 x 0.25
= 3.25 ℓ
Volume of water that Valen had at first
= 13 B + 2
= 13 x 0.25 + 2
= 3.25 + 2
= 5.25 ℓ
Total volume of water that Valen and Howard had at first
= 2 x 5.25
= 10.5 ℓ
Answer(s): (a) 250 mℓ; (b) 10.5 ℓ
