Sam and Vincent each had the same volume of water. The water was used to pour into identical bottles. Sam filled up 16 bottles and had 7 ℓ of water left. Vincent filled up 12 bottles and had 8.6 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Sam and Vincent had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Sam had = 16 B + 7 --- (1)
Volume of water that Vincent had = 12 B + 8.6 --- (2)
The volume of water that Sam and Vincent have is the same.
(1) = (2)
16 B + 7 = 12 B + 8.6
16 B - 12 B = 8.6 - 7
4 B = 1.6
1 B = 1.6 ÷ 4 = 0.4
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
(b)
Volume of 16 bottles
= 16 x 0.4
= 6.4 ℓ
Volume of water that Sam had at first
= 16 B + 7
= 16 x 0.4 + 7
= 6.4 + 7
= 13.4 ℓ
Total volume of water that Sam and Vincent had at first
= 2 x 13.4
= 26.8 ℓ
Answer(s): (a) 400 mℓ; (b) 26.8 ℓ
