A chemist needs 130 millimeters of a 49% solution but has only 24% and 89% solutions available. Find how many millimeters of each that should be mixed to get desired solution. 

To solve this problem, let's denote:

- \( x \) = the amount of the 24% solution needed (in milliliters)
- \( y \) = the amount of the 89% solution needed (in milliliters)

The chemist needs a total of 130 milliliters of a 49% solution. This gives us the following two equations:

1. **Total volume equation**:
   \[
   x + y = 130
   \]

2. **Concentration equation**:
   \[
   0.24x + 0.89y = 0.49 \times 130
   \]

Let's solve these equations step by step.

### Step 1: Express \( y \) in terms of \( x \) from the first equation
\[
y = 130 - x
\]

### Step 2: Substitute \( y \) in the concentration equation
\[
0.24x + 0.89(130 - x) = 63.7
\]

### Step 3: Expand and simplify the equation
\[
0.24x + 115.7 - 0.89x = 63.7
\]
\[
-0.65x + 115.7 = 63.7
\]

### Step 4: Solve for \( x \)
\[
-0.65x = 63.7 - 115.7
\]
\[
-0.65x = -52
\]
\[
x = \frac{-52}{-0.65} = 80
\]

So, \( x = 80 \) milliliters of the 24% solution.

### Step 5: Find \( y \) using \( x \)
\[
y = 130 - 80 = 50
\]

So, \( y = 50 \) milliliters of the 89% solution.

### Final Answer:
The chemist should mix 80 milliliters of the 24% solution with 50 milliliters of the 89% solution to obtain 130 milliliters of a 49% solution.

Would you like more details or have any questions?

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Here are five related questions to deepen your understanding:

1. How would the solution change if a different concentration of the final mixture was required?
2. What happens if the chemist has only a 40% and 70% solution available?
3. How would you adjust the volumes if the chemist needed 200 milliliters instead of 130 milliliters?
4. How does this method apply to mixtures with three or more different concentrations?
5. Can you generalize a formula for any two solutions mixed to achieve a desired concentration?

**Tip:** Always verify your solution by checking if the final concentrations add up correctly when mixed.

A chemist needs 130 milliliters of a 49% solution but has only 24% and 89% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Learn how to solve a system of linear equations to mix 24% and 89% solutions for a desired 49% concentration. This step-by-step guide helps chemists calculate the exact amounts of each solution. Suitable for students in Grades 8-10.

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