Carl and Tom each had the same volume of water. The water was used to pour into identical bottles. Carl filled up 15 bottles and had 6 ℓ of water left. Tom filled up 11 bottles and had 8 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Carl and Tom had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Carl had = 15 B + 6 --- (1)
Volume of water that Tom had = 11 B + 8 --- (2)
The volume of water that Carl and Tom have is the same.
(1) = (2)
15 B + 6 = 11 B + 8
15 B - 11 B = 8 - 6
4 B = 2
1 B = 2 ÷ 4 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 15 bottles
= 15 x 0.5
= 7.5 ℓ
Volume of water that Carl had at first
= 15 B + 6
= 15 x 0.5 + 6
= 7.5 + 6
= 13.5 ℓ
Total volume of water that Carl and Tom had at first
= 2 x 13.5
= 27 ℓ
Answer(s): (a) 500 mℓ; (b) 27 ℓ
