Joan has 40 liters of a 25% solution. How many liters of a 60% solution should she add to make a 30% solution?
C1 x V1 + C2 x V2 = C3 x (V1+V2)
0.25 x 40 + 0.60 x V2 = 0.30 x (40+V2)
10 + 0.60V2 = 12 + 0.30V2
0.30V2 = 2
V2 = 20/3 litres
Let the number of litres of the 60% solution be x
.25(40) + .6x = .3(40+x)
solve for x
To solve this problem, we can use the concept of mixing solutions with different concentrations.
Let's break down the problem and analyze the given information:
Joan has 40 liters of a 25% solution.
Let's call this solution "Solution A."
Now, Joan wants to add a second solution, which is a 60% solution.
Let's call this solution "Solution B."
She wants to end up with a 30% solution.
Let's call this final mixture "Solution C."
To solve the problem, we need to determine how many liters of Solution B Joan should add to Solution A to obtain Solution C.
Let's start by calculating the amount of the active ingredient (we can assume it's the same for both solutions) in each solution:
For Solution A:
Amount of active ingredient = 40 liters * 0.25 (25% expressed as a decimal) = 10 liters
For Solution B:
Assume Joan adds "x" liters of Solution B to the mixture.
The amount of active ingredient = x liters * 0.60 (60% expressed as a decimal) = 0.6x liters.
For Solution C:
To obtain a 30% solution, the total amount of active ingredient in Solution C should be equal to the sum of the amounts of the active ingredient in Solution A and Solution B.
Amount of active ingredient in Solution C = 10 liters + 0.6x liters
Since we want a 30% solution, the total volume of the final mixture (Solution C) would be equal to 40 liters (from Solution A) plus "x" liters (from Solution B). This gives us:
Total volume of Solution C = 40 liters + x liters = 40 + x liters
Since the amount of the active ingredient in Solution C should be equal to 30% of the total volume of Solution C, we can set up an equation:
Amount of active ingredient in Solution C = 0.30 * Total volume of Solution C
10 liters + 0.6x liters = 0.30 * (40 + x) liters
Now, we can solve for "x" to find out how many liters of Solution B Joan should add:
10 + 0.6x = 0.30 * (40 + x)
10 + 0.6x = 12 + 0.3x
0.6x - 0.3x = 12 - 10
0.3x = 2
x = 2 / 0.3
x = 6.666...
Thus, Joan should add approximately 6.67 liters of the 60% solution (Solution B) to make a 30% solution (Solution C).