Valen and Bobby each had the same volume of water. The water was used to pour into identical bottles. Valen filled up 15 bottles and had 8 ℓ of water left. Bobby filled up 11 bottles and had 10 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 Bobby 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 = 15 B + 8 --- (1)
Volume of water that Bobby had = 11 B + 10 --- (2)
The volume of water that Valen and Bobby have is the same.
(1) = (2)
15 B + 8 = 11 B + 10
15 B - 11 B = 10 - 8
4 B = 2
1 B = 2 ÷ 4 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 15 bottles
= 15 x 0.5
= 7.5 ℓ
Volume of water that Valen had at first
= 15 B + 8
= 15 x 0.5 + 8
= 7.5 + 8
= 15.5 ℓ
Total volume of water that Valen and Bobby had at first
= 2 x 15.5
= 31 ℓ
Answer(s): (a) 500 mℓ; (b) 31 ℓ
