Zane and Mark each had the same volume of water. The water was used to pour into identical bottles. Zane filled up 12 bottles and had 6 ℓ of water left. Mark filled up 10 bottles and had 7 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Zane and Mark had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Zane had = 12 B + 6 --- (1)
Volume of water that Mark had = 10 B + 7 --- (2)
The volume of water that Zane and Mark have is the same.
(1) = (2)
12 B + 6 = 10 B + 7
12 B - 10 B = 7 - 6
2 B = 1
1 B = 1 ÷ 2 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 12 bottles
= 12 x 0.5
= 6 ℓ
Volume of water that Zane had at first
= 12 B + 6
= 12 x 0.5 + 6
= 6 + 6
= 12 ℓ
Total volume of water that Zane and Mark had at first
= 2 x 12
= 24 ℓ
Answer(s): (a) 500 mℓ; (b) 24 ℓ