Bleach Solution
| | Cups | Bleach Concentration | Total |
| :---- | :--- | :------------------- | :---- |
| 10% Bleach | 5 | 0.10 | 0.5 |
| 25% Bleach | $x$ | 0.25 | 0.25x |
| Mixture | $5+x$ | 0.20 | 3 |
What is the value of $x$?
A. 1
B. 3
C. 10
D. 24
Answer (2)
Calculate the amount of bleach in the 10% solution: 5 cups × 0.10 = 0.5 cups .
Express the amount of bleach in the 25% solution: 0.25 x .
Set up the equation: 0.5 + 0.25 x = 3 .
Solve for x : x = 0.25 2.5 = 10 . The value of x is 10 .
Explanation
Understanding the Problem We are given a table describing a mixture of two bleach solutions. The goal is to find the value of x , which represents the number of cups of the 25% bleach solution. We can set up an equation based on the total amount of bleach in the mixture.
Calculating Bleach Amounts The total amount of bleach in the 10% solution is 5 cups × 0.10 = 0.5 cups . The total amount of bleach in the 25% solution is x cups × 0.25 = 0.25 x cups . The total amount of bleach in the mixture is ( 5 + x ) cups × 0.20 = 3 cups .
Setting up the Equation We can set up the equation: 0.5 + 0.25 x = 3
Isolating the x term Now, we solve for x . First, subtract 0.5 from both sides of the equation: 0.25 x = 3 − 0.5 0.25 x = 2.5
Solving for x Next, divide both sides by 0.25: x = 0.25 2.5 x = 10
Final Answer Therefore, the value of x is 10.
Examples
Imagine you're mixing cleaning solutions, and you need a specific concentration for a task. This problem is similar to calculating how much of each solution to mix to achieve the desired concentration. Understanding how to solve such problems is crucial in various fields, including chemistry, cooking, and even in everyday tasks like diluting concentrates.
By setting up equations based on the amounts of bleach in each solution and the desired concentration in the mixture, we find that the value of x is 10 cups. Thus, the answer to the question is C. 10 .
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