Bobby and Glen each had the same volume of water. The water was used to pour into identical bottles. Bobby filled up 17 bottles and had 8 ℓ of water left. Glen filled up 13 bottles and had 9.6 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 Glen 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 = 17 B + 8 --- (1)
Volume of water that Glen had = 13 B + 9.6 --- (2)
The volume of water that Bobby and Glen have is the same.
(1) = (2)
17 B + 8 = 13 B + 9.6
17 B - 13 B = 9.6 - 8
4 B = 1.6
1 B = 1.6 ÷ 4 = 0.4
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
(b)
Volume of 17 bottles
= 17 x 0.4
= 6.8 ℓ
Volume of water that Bobby had at first
= 17 B + 8
= 17 x 0.4 + 8
= 6.8 + 8
= 14.8 ℓ
Total volume of water that Bobby and Glen had at first
= 2 x 14.8
= 29.6 ℓ
Answer(s): (a) 400 mℓ; (b) 29.6 ℓ