Dylan and Michael each had the same volume of water. The water was used to pour into identical bottles. Dylan filled up 19 bottles and had 4 ℓ of water left. Michael filled up 13 bottles and had 4.72 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Dylan and Michael had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Dylan had = 19 B + 4 --- (1)
Volume of water that Michael had = 13 B + 4.72 --- (2)
The volume of water that Dylan and Michael have is the same.
(1) = (2)
19 B + 4 = 13 B + 4.72
19 B - 13 B = 4.72 - 4
6 B = 0.72
1 B = 0.72 ÷ 6 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 19 bottles
= 19 x 0.12
= 2.28 ℓ
Volume of water that Dylan had at first
= 19 B + 4
= 19 x 0.12 + 4
= 2.28 + 4
= 6.28 ℓ
Total volume of water that Dylan and Michael had at first
= 2 x 6.28
= 12.56 ℓ
Answer(s): (a) 120 mℓ; (b) 12.56 ℓ
