Pierre and Zeph each had the same volume of water. The water was used to pour into identical bottles. Pierre filled up 12 bottles and had 3 ℓ of water left. Zeph filled up 10 bottles and had 3.28 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Pierre and Zeph had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Pierre had = 12 B + 3 --- (1)
Volume of water that Zeph had = 10 B + 3.28 --- (2)
The volume of water that Pierre and Zeph have is the same.
(1) = (2)
12 B + 3 = 10 B + 3.28
12 B - 10 B = 3.28 - 3
2 B = 0.28
1 B = 0.28 ÷ 2 = 0.14
1 ℓ = 1000 mℓ
0.14 ℓ = 0.14 x 1000 = 140 mℓ
(b)
Volume of 12 bottles
= 12 x 0.14
= 1.68 ℓ
Volume of water that Pierre had at first
= 12 B + 3
= 12 x 0.14 + 3
= 1.68 + 3
= 4.68 ℓ
Total volume of water that Pierre and Zeph had at first
= 2 x 4.68
= 9.36 ℓ
Answer(s): (a) 140 mℓ; (b) 9.36 ℓ
