Elijah and Jack each had the same volume of water. The water was used to pour into identical bottles. Elijah filled up 9 bottles and had 6 ℓ of water left. Jack filled up 7 bottles and had 6.4 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 Jack 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 = 9 B + 6 --- (1)
Volume of water that Jack had = 7 B + 6.4 --- (2)
The volume of water that Elijah and Jack have is the same.
(1) = (2)
9 B + 6 = 7 B + 6.4
9 B - 7 B = 6.4 - 6
2 B = 0.4
1 B = 0.4 ÷ 2 = 0.2
1 ℓ = 1000 mℓ
0.2 ℓ = 0.2 x 1000 = 200 mℓ
(b)
Volume of 9 bottles
= 9 x 0.2
= 1.8 ℓ
Volume of water that Elijah had at first
= 9 B + 6
= 9 x 0.2 + 6
= 1.8 + 6
= 7.8 ℓ
Total volume of water that Elijah and Jack had at first
= 2 x 7.8
= 15.6 ℓ
Answer(s): (a) 200 mℓ; (b) 15.6 ℓ
