Peter and Mark each had the same volume of water. The water was used to pour into identical bottles. Peter filled up 19 bottles and had 5 ℓ of water left. Mark filled up 13 bottles and had 6.32 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Peter and Mark had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Peter had = 19 B + 5 --- (1)
Volume of water that Mark had = 13 B + 6.32 --- (2)
The volume of water that Peter and Mark have is the same.
(1) = (2)
19 B + 5 = 13 B + 6.32
19 B - 13 B = 6.32 - 5
6 B = 1.32
1 B = 1.32 ÷ 6 = 0.22
1 ℓ = 1000 mℓ
0.22 ℓ = 0.22 x 1000 = 220 mℓ
(b)
Volume of 19 bottles
= 19 x 0.22
= 4.18 ℓ
Volume of water that Peter had at first
= 19 B + 5
= 19 x 0.22 + 5
= 4.18 + 5
= 9.18 ℓ
Total volume of water that Peter and Mark had at first
= 2 x 9.18
= 18.36 ℓ
Answer(s): (a) 220 mℓ; (b) 18.36 ℓ
