Bobby and Elijah each had the same volume of water. The water was used to pour into identical bottles. Bobby filled up 16 bottles and had 8 ℓ of water left. Elijah filled up 12 bottles and had 8.6 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Bobby 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 Bobby had = 16 B + 8 --- (1)
Volume of water that Elijah had = 12 B + 8.6 --- (2)
The volume of water that Bobby and Elijah have is the same.
(1) = (2)
16 B + 8 = 12 B + 8.6
16 B - 12 B = 8.6 - 8
4 B = 0.6
1 B = 0.6 ÷ 4 = 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 Bobby had at first
= 16 B + 8
= 16 x 0.15 + 8
= 2.4 + 8
= 10.4 ℓ
Total volume of water that Bobby and Elijah had at first
= 2 x 10.4
= 20.8 ℓ
Answer(s): (a) 150 mℓ; (b) 20.8 ℓ
