Seth and Simon each had the same volume of water. The water was used to pour into identical bottles. Seth filled up 13 bottles and had 7 ℓ of water left. Simon filled up 9 bottles and had 7.48 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Seth and Simon had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Seth had = 13 B + 7 --- (1)
Volume of water that Simon had = 9 B + 7.48 --- (2)
The volume of water that Seth and Simon have is the same.
(1) = (2)
13 B + 7 = 9 B + 7.48
13 B - 9 B = 7.48 - 7
4 B = 0.48
1 B = 0.48 ÷ 4 = 0.12
1 ℓ = 1000 mℓ
0.12 ℓ = 0.12 x 1000 = 120 mℓ
(b)
Volume of 13 bottles
= 13 x 0.12
= 1.56 ℓ
Volume of water that Seth had at first
= 13 B + 7
= 13 x 0.12 + 7
= 1.56 + 7
= 8.56 ℓ
Total volume of water that Seth and Simon had at first
= 2 x 8.56
= 17.12 ℓ
Answer(s): (a) 120 mℓ; (b) 17.12 ℓ
