How many quarts of pure antifreeze solution must be added to 5 quarts of a 10% antifreeze solution to obtain a 40% antifreeze solution

To solve this problem, let's use algebra to set up an equation. 

Let \( x \) represent the number of quarts of pure antifreeze solution that must be added.

### Step 1: Determine the amount of antifreeze in the existing solution.
- The current solution is 5 quarts of a 10% antifreeze solution.
- The amount of pure antifreeze in this solution is \( 0.1 \times 5 = 0.5 \) quarts.

### Step 2: Set up the equation.
- After adding \( x \) quarts of pure antifreeze, the total amount of the solution becomes \( 5 + x \) quarts.
- The amount of pure antifreeze in the new solution is \( 0.5 + x \) quarts.
- We want the final solution to be 40% antifreeze, so:
  \[
  \frac{0.5 + x}{5 + x} = 0.4
  \]

### Step 3: Solve the equation.
1. Multiply both sides by \( 5 + x \) to eliminate the fraction:
   \[
   0.5 + x = 0.4(5 + x)
   \]
2. Distribute the 0.4 on the right side:
   \[
   0.5 + x = 2 + 0.4x
   \]
3. Subtract \( 0.4x \) from both sides:
   \[
   0.6x = 1.5
   \]
4. Divide both sides by 0.6:
   \[
   x = \frac{1.5}{0.6} = 2.5
   \]

### Final Answer:
You must add **2.5 quarts** of pure antifreeze solution to obtain a 40% antifreeze solution.

Would you like any details on this process or have further questions?

Here are some related problems you might find interesting:
1. What is the concentration of antifreeze if 1 quart of pure antifreeze is added to the original solution?
2. How much 50% antifreeze solution should be added to achieve a 30% solution?
3. If 10 quarts of a 5% antifreeze solution is added instead, what would the final concentration be?
4. How much pure water must be added to dilute the original 10% solution to 5%?
5. What is the final volume if 3 quarts of pure antifreeze are added?

**Tip:** When solving mixture problems, setting up a clear equation that represents the relationship between the quantities and their concentrations is crucial.

Learn how to solve a mixture problem involving antifreeze concentrations. Find out how many quarts of pure antifreeze solution must be added to a 5-quart 10% antifreeze solution to achieve a 40% antifreeze solution. Suitable for high school students and those interested in mathematical problem-solving.

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