Jeremy and Tim each had the same volume of water. The water was used to pour into identical bottles. Jeremy filled up 16 bottles and had 3 ℓ of water left. Tim filled up 12 bottles and had 3.88 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Jeremy and Tim had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Jeremy had = 16 B + 3 --- (1)
Volume of water that Tim had = 12 B + 3.88 --- (2)
The volume of water that Jeremy and Tim have is the same.
(1) = (2)
16 B + 3 = 12 B + 3.88
16 B - 12 B = 3.88 - 3
4 B = 0.88
1 B = 0.88 ÷ 4 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 16 bottles
= 16 x 0.22
= 3.52 ℓ
Volume of water that Jeremy had at first
= 16 B + 3
= 16 x 0.22 + 3
= 3.52 + 3
= 6.52 ℓ
Total volume of water that Jeremy and Tim had at first
= 2 x 6.52
= 13.04 ℓ
Answer(s): (a) 220 mℓ; (b) 13.04 ℓ
