John and Justin each had the same volume of water. The water was used to pour into identical bottles. John filled up 17 bottles and had 3 ℓ of water left. Justin filled up 13 bottles and had 3.44 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water John and Justin had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that John had = 17 B + 3 --- (1)
Volume of water that Justin had = 13 B + 3.44 --- (2)
The volume of water that John and Justin have is the same.
(1) = (2)
17 B + 3 = 13 B + 3.44
17 B - 13 B = 3.44 - 3
4 B = 0.44
1 B = 0.44 ÷ 4 = 0.11
1 ℓ = 1000 mℓ
0.11 ℓ = 0.11 x 1000 = 110 mℓ
(b)
Volume of 17 bottles
= 17 x 0.11
= 1.87 ℓ
Volume of water that John had at first
= 17 B + 3
= 17 x 0.11 + 3
= 1.87 + 3
= 4.87 ℓ
Total volume of water that John and Justin had at first
= 2 x 4.87
= 9.74 ℓ
Answer(s): (a) 110 mℓ; (b) 9.74 ℓ
