Neave and Justin each had the same volume of water. The water was used to pour into identical bottles. Neave filled up 17 bottles and had 3 ℓ of water left. Justin filled up 13 bottles and had 4 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Neave and Justin had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Neave had = 17 B + 3 --- (1)
Volume of water that Justin had = 13 B + 4 --- (2)
The volume of water that Neave and Justin have is the same.
(1) = (2)
17 B + 3 = 13 B + 4
17 B - 13 B = 4 - 3
4 B = 1
1 B = 1 ÷ 4 = 0.25
1 ℓ = 1000 mℓ
0.25 ℓ = 0.25 x 1000 = 250 mℓ
(b)
Volume of 17 bottles
= 17 x 0.25
= 4.25 ℓ
Volume of water that Neave had at first
= 17 B + 3
= 17 x 0.25 + 3
= 4.25 + 3
= 7.25 ℓ
Total volume of water that Neave and Justin had at first
= 2 x 7.25
= 14.5 ℓ
Answer(s): (a) 250 mℓ; (b) 14.5 ℓ