Jenson and Mark each had the same volume of water. The water was used to pour into identical bottles. Jenson filled up 9 bottles and had 6 ℓ of water left. Mark filled up 7 bottles and had 7 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Jenson 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 Jenson had = 9 B + 6 --- (1)
Volume of water that Mark had = 7 B + 7 --- (2)
The volume of water that Jenson and Mark have is the same.
(1) = (2)
9 B + 6 = 7 B + 7
9 B - 7 B = 7 - 6
2 B = 1
1 B = 1 ÷ 2 = 0.5
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
(b)
Volume of 9 bottles
= 9 x 0.5
= 4.5 ℓ
Volume of water that Jenson had at first
= 9 B + 6
= 9 x 0.5 + 6
= 4.5 + 6
= 10.5 ℓ
Total volume of water that Jenson and Mark had at first
= 2 x 10.5
= 21 ℓ
Answer(s): (a) 500 mℓ; (b) 21 ℓ
