Tim and Sean each had the same volume of water. The water was used to pour into identical bottles. Tim filled up 11 bottles and had 8 ℓ of water left. Sean filled up 9 bottles and had 8.26 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Tim and Sean had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Tim had = 11 B + 8 --- (1)
Volume of water that Sean had = 9 B + 8.26 --- (2)
The volume of water that Tim and Sean have is the same.
(1) = (2)
11 B + 8 = 9 B + 8.26
11 B - 9 B = 8.26 - 8
2 B = 0.26
1 B = 0.26 ÷ 2 = 0.13
1 ℓ = 1000 mℓ
0.13 ℓ = 0.13 x 1000 = 130 mℓ
(b)
Volume of 11 bottles
= 11 x 0.13
= 1.43 ℓ
Volume of water that Tim had at first
= 11 B + 8
= 11 x 0.13 + 8
= 1.43 + 8
= 9.43 ℓ
Total volume of water that Tim and Sean had at first
= 2 x 9.43
= 18.86 ℓ
Answer(s): (a) 130 mℓ; (b) 18.86 ℓ
