40% of k liters of acid are added to 60% of w liters of water. Write an algebraic expression for the total volume of the solution.
Answer is good up to (0.4k+0.6w) L.
Since we do not know the values of k nor w, their coefficients cannot be added together.
The correct answer would be
(0.4k+0.6w) L.
(0.4k+0.6w)
Well, if we add 40% of k liters of acid to 60% of w liters of water, we can think of it as mixing lemon juice and water to make a refreshing lemonade! The total volume of the solution can be expressed as:
(k * 0.4) + (w * 0.6)
So, the algebraic expression for the total volume of the solution is (0.4k + 0.6w). Voilà, we've got ourselves a tangy equation!
To write an algebraic expression for the total volume of the solution, we can start by calculating the volume of acid added and the volume of water used.
Given that 40% of k liters of acid is added, we can calculate the volume of acid in the solution as (40/100) * k, which simplifies to 0.4k liters.
Similarly, 60% of w liters of water is used, so the volume of water in the solution is (60/100) * w, which simplifies to 0.6w liters.
To find the total volume of the solution, we add the volume of acid and the volume of water:
Total volume = Volume of acid + Volume of water
= 0.4k + 0.6w
Therefore, the algebraic expression for the total volume of the solution is 0.4k + 0.6w.
Example to help you:
30% of 4L of orange juice is added to 70% of 5L of grapefruit juice, find the total volume.
Volume of orange juice = 30% of 4L
=0.30*4
=1.2L
Volume of grapefruit juice=70% of 5L
=0.7*5
=3.5L
Total volume = 1.2L+3.5L=4.7L
40% of k liters
0.40*kL
0.60*wL
0.40kL + 0.60wL = 1wL
is this the correct answer