Justin and Rael each had the same volume of water. The water was used to pour into identical bottles. Justin filled up 10 bottles and had 4 ℓ of water left. Rael filled up 8 bottles and had 4.28 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Justin and Rael had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Justin had = 10 B + 4 --- (1)
Volume of water that Rael had = 8 B + 4.28 --- (2)
The volume of water that Justin and Rael have is the same.
(1) = (2)
10 B + 4 = 8 B + 4.28
10 B - 8 B = 4.28 - 4
2 B = 0.28
1 B = 0.28 ÷ 2 = 0.14
1 ℓ = 1000 mℓ
0.14 ℓ = 0.14 x 1000 = 140 mℓ
(b)
Volume of 10 bottles
= 10 x 0.14
= 1.4 ℓ
Volume of water that Justin had at first
= 10 B + 4
= 10 x 0.14 + 4
= 1.4 + 4
= 5.4 ℓ
Total volume of water that Justin and Rael had at first
= 2 x 5.4
= 10.8 ℓ
Answer(s): (a) 140 mℓ; (b) 10.8 ℓ
