A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an [tex]$8 \%$[/tex] solution. The table shows the amount of each solution used in the mixture.
Peroxide Solution
| | Liters of Solution | Peroxide Concentration | Total |
| :------------------ | :----------------- | :--------------------- | :---- |
| 4\% Peroxide | 100-s | 0.04 | x |
| 10\% Peroxide | s | 0.10 | y |
| Mixture | 100 | 0.08 | z |
What is the value of [tex]$z$[/tex] in the table?
Answer (1)
The problem requires finding the total amount of peroxide in a mixture.
Multiply the total volume of the mixture (100 L) by the concentration of the mixture (0.08).
Calculate the total amount of peroxide: 100 × 0.08 = 8 .
The value of z is 8 .
Explanation
Understanding the Problem We are given a mixture problem where a 4% peroxide solution is mixed with a 10% peroxide solution to create 100 L of an 8% solution. We need to find the value of z in the table, which represents the total amount of peroxide in the mixture.
Calculating Total Peroxide To find the total amount of peroxide in the mixture, we multiply the total volume of the mixture by the concentration of the mixture. The total volume is 100 L and the concentration is 8%, or 0.08.
Finding the Value of z Therefore, z = 100 L × 0.08 = 8 L .
Final Answer The value of z in the table is 8.
Examples
Imagine you're a pharmacist mixing different concentrations of a medication to get the precise dosage needed for a patient. This problem is similar to calculating the final concentration of a mixture when you combine solutions of different strengths. Understanding how to calculate the final concentration helps ensure the patient receives the correct amount of medication, avoiding under- or over-dosage. For example, mixing saline solutions of different concentrations to achieve a specific isotonic solution for intravenous administration.
