Jeremy and Caden each had the same volume of water. The water was used to pour into identical bottles. Jeremy filled up 12 bottles and had 7 ℓ of water left. Caden filled up 10 bottles and had 7.26 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Jeremy and Caden had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Jeremy had = 12 B + 7 --- (1)
Volume of water that Caden had = 10 B + 7.26 --- (2)
The volume of water that Jeremy and Caden have is the same.
(1) = (2)
12 B + 7 = 10 B + 7.26
12 B - 10 B = 7.26 - 7
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 12 bottles
= 12 x 0.13
= 1.56 ℓ
Volume of water that Jeremy had at first
= 12 B + 7
= 12 x 0.13 + 7
= 1.56 + 7
= 8.56 ℓ
Total volume of water that Jeremy and Caden had at first
= 2 x 8.56
= 17.12 ℓ
Answer(s): (a) 130 mℓ; (b) 17.12 ℓ
