Ben and Andy each had the same volume of water. The water was used to pour into identical bottles. Ben filled up 15 bottles and had 4 ℓ of water left. Andy filled up 11 bottles and had 4.6 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Ben and Andy had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Ben had = 15 B + 4 --- (1)
Volume of water that Andy had = 11 B + 4.6 --- (2)
The volume of water that Ben and Andy have is the same.
(1) = (2)
15 B + 4 = 11 B + 4.6
15 B - 11 B = 4.6 - 4
4 B = 0.6
1 B = 0.6 ÷ 4 = 0.15
1 ℓ = 1000 mℓ
0.15 ℓ = 0.15 x 1000 = 150 mℓ
(b)
Volume of 15 bottles
= 15 x 0.15
= 2.25 ℓ
Volume of water that Ben had at first
= 15 B + 4
= 15 x 0.15 + 4
= 2.25 + 4
= 6.25 ℓ
Total volume of water that Ben and Andy had at first
= 2 x 6.25
= 12.5 ℓ
Answer(s): (a) 150 mℓ; (b) 12.5 ℓ
