Elijah and Jenson each had the same volume of water. The water was used to pour into identical bottles. Elijah filled up 18 bottles and had 7 ℓ of water left. Jenson filled up 14 bottles and had 7.8 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Elijah and Jenson had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Elijah had = 18 B + 7 --- (1)
Volume of water that Jenson had = 14 B + 7.8 --- (2)
The volume of water that Elijah and Jenson have is the same.
(1) = (2)
18 B + 7 = 14 B + 7.8
18 B - 14 B = 7.8 - 7
4 B = 0.8
1 B = 0.8 ÷ 4 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 18 bottles
= 18 x 0.2
= 3.6 ℓ
Volume of water that Elijah had at first
= 18 B + 7
= 18 x 0.2 + 7
= 3.6 + 7
= 10.6 ℓ
Total volume of water that Elijah and Jenson had at first
= 2 x 10.6
= 21.2 ℓ
Answer(s): (a) 200 mℓ; (b) 21.2 ℓ
