Sam and Ethan each had the same volume of water. The water was used to pour into identical bottles. Sam filled up 16 bottles and had 5 ℓ of water left. Ethan filled up 10 bottles and had 5.9 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 Ethan 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 + 5 --- (1)
Volume of water that Ethan had = 10 B + 5.9 --- (2)
The volume of water that Sam and Ethan have is the same.
(1) = (2)
16 B + 5 = 10 B + 5.9
16 B - 10 B = 5.9 - 5
6 B = 0.9
1 B = 0.9 ÷ 6 = 0.15
1 ℓ = 1000 mℓ
0.15 ℓ = 0.15 x 1000 = 150 mℓ
(b)
Volume of 16 bottles
= 16 x 0.15
= 2.4 ℓ
Volume of water that Sam had at first
= 16 B + 5
= 16 x 0.15 + 5
= 2.4 + 5
= 7.4 ℓ
Total volume of water that Sam and Ethan had at first
= 2 x 7.4
= 14.8 ℓ
Answer(s): (a) 150 mℓ; (b) 14.8 ℓ
