Rael and Carl each had the same volume of water. The water was used to pour into identical bottles. Rael filled up 19 bottles and had 8 ℓ of water left. Carl filled up 13 bottles and had 8.78 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Rael and Carl had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Rael had = 19 B + 8 --- (1)
Volume of water that Carl had = 13 B + 8.78 --- (2)
The volume of water that Rael and Carl have is the same.
(1) = (2)
19 B + 8 = 13 B + 8.78
19 B - 13 B = 8.78 - 8
6 B = 0.78
1 B = 0.78 ÷ 6 = 0.13
1 ℓ = 1000 mℓ
0.13 ℓ = 0.13 x 1000 = 130 mℓ
(b)
Volume of 19 bottles
= 19 x 0.13
= 2.47 ℓ
Volume of water that Rael had at first
= 19 B + 8
= 19 x 0.13 + 8
= 2.47 + 8
= 10.47 ℓ
Total volume of water that Rael and Carl had at first
= 2 x 10.47
= 20.94 ℓ
Answer(s): (a) 130 mℓ; (b) 20.94 ℓ
