To conduct a new experiment, a scientist needs a 23% salt water solution. How much of a 13% solution must be mixed with 45 quarts of a 32% solution to get the proper solution?
.13A+.32*45=.23(A+45)
can you solve for the volume of A?
actually this is only freshman (HS) math but i still don't remember how to do it
To find the amount of a 13% salt water solution needed to mix with a 32% solution in order to obtain a 23% solution, we can use the concept of the concentration of the solution.
Let's assume that x represents the amount of the 13% salt water solution that needs to be added.
Now, let's break down the question:
1. Given: The scientist needs a 23% salt water solution.
2. Given: There are 45 quarts of a 32% solution.
3. Given: There is a 13% solution available.
To solve the problem, we will use the following formula to calculate the concentration of the mixture:
(Concentration A * Volume A) + (Concentration B * Volume B) = (Concentration C * Volume C)
Where:
- Concentration A is the concentration of the first solution (32% in this case).
- Volume A is the volume of the first solution (45 quarts in this case).
- Concentration B is the concentration of the second solution (13% in this case).
- Volume B is the volume of the second solution (x quarts in this case).
- Concentration C is the desired concentration of the resultant mixture (23% in this case).
- Volume C is the total volume of the resultant mixture (45 + x quarts in this case).
Using the formula, we can write the equation as:
(0.32 * 45) + (0.13 * x) = (0.23 * (45 + x))
Now we can solve for x:
14.4 + 0.13x = 10.35 + 0.23x
Rearranging the equation:
0.23x - 0.13x = 14.4 - 10.35
0.10x = 4.05
Dividing both sides by 0.10:
x = 4.05 / 0.10
x = 40.5
Therefore, 40.5 quarts of the 13% salt water solution must be mixed with 45 quarts of the 32% solution to obtain the desired 23% salt water solution.