Brandon and Elijah each had the same volume of water. The water was used to pour into identical bottles. Brandon filled up 10 bottles and had 3 ℓ of water left. Elijah filled up 8 bottles and had 3.26 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Brandon and Elijah had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Brandon had = 10 B + 3 --- (1)
Volume of water that Elijah had = 8 B + 3.26 --- (2)
The volume of water that Brandon and Elijah have is the same.
(1) = (2)
10 B + 3 = 8 B + 3.26
10 B - 8 B = 3.26 - 3
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 10 bottles
= 10 x 0.13
= 1.3 ℓ
Volume of water that Brandon had at first
= 10 B + 3
= 10 x 0.13 + 3
= 1.3 + 3
= 4.3 ℓ
Total volume of water that Brandon and Elijah had at first
= 2 x 4.3
= 8.6 ℓ
Answer(s): (a) 130 mℓ; (b) 8.6 ℓ
