I need help figuring out equations for a math problem. This is the question:
For a chemistry experiment Marie needs 300 ml of a 15% acid solution.
The Science Department has quantities of 5% acid solution and 20% acid solution.
What volume of each solution is required to mix together to get her required
concentration?
I tried my best to come up with two equations needed to solve this problem and need help confirming whether or not it is correct. I don't need the problem solved just help in finding out the equations to solve the problem. If the equations I provided are not correct then if anybody could help me understand why they aren't correct and what is the correct answer and how you came to that conclusion? Thank you!
x + y = 300
0.05x + 0.2y = 0.15
BUT
0.05x + 0.2y = 0.15 * 300
!!!!!
Your equations are correct! Let's break them down and understand why.
First, let's define our variables:
Let x represent the volume (in ml) of the 5% acid solution.
Let y represent the volume (in ml) of the 20% acid solution.
Now, let's analyze the problem and derive the equations:
1. Equation 1: x + y = 300
The sum of the volumes of the two solutions (x and y) should be equal to the desired total volume of 300 ml.
2. Equation 2: 0.05x + 0.2y = 0.15
The concentration of the acid in the final mixture should be 15%. Therefore, we need to consider the amount of acid present in each solution and ensure that the sum of these amounts, when scaled by their respective volumes, equals 15% of the total volume.
- The acid amount in the 5% solution is 0.05x (5% of x).
- The acid amount in the 20% solution is 0.2y (20% of y).
- The total acid amount in the final mixture is 0.15 (15% of 300ml).
Hence, the equation becomes 0.05x + 0.2y = 0.15.
To solve the equations, you can use various methods, such as substitution, elimination, or graphing.