Tommy and Reggie each had the same volume of water. The water was used to pour into identical bottles. Tommy filled up 9 bottles and had 5 ℓ of water left. Reggie filled up 7 bottles and had 5.22 ℓ of water left.
- What was the capacity of each bottle? Give your answer in millilitres.
- What was the total volume of water Tommy and Reggie had at first? Give your answer in litres.
(a)
Let 1 B be the volume of 1 bottle of water.
Volume of water that Tommy had = 9 B + 5 --- (1)
Volume of water that Reggie had = 7 B + 5.22 --- (2)
The volume of water that Tommy and Reggie have is the same.
(1) = (2)
9 B + 5 = 7 B + 5.22
9 B - 7 B = 5.22 - 5
2 B = 0.22
1 B = 0.22 ÷ 2 = 0.11
1 ℓ = 1000 mℓ
0.11 ℓ = 0.11 x 1000 = 110 mℓ
(b)
Volume of 9 bottles
= 9 x 0.11
= 0.99 ℓ
Volume of water that Tommy had at first
= 9 B + 5
= 9 x 0.11 + 5
= 0.99 + 5
= 5.99 ℓ
Total volume of water that Tommy and Reggie had at first
= 2 x 5.99
= 11.98 ℓ
Answer(s): (a) 110 mℓ; (b) 11.98 ℓ
