1qt of a 40% sugar solution was mixed with 6qt of a 82% sugar solution.Find the concentration of the new mixture

To find the concentration of sugar in the new mixture, we'll use the concept of weighted averages. The total amount of sugar in each solution will be added together and divided by the total volume of the solution.

### Step 1: Calculate the amount of sugar in each solution
- The 40% solution contains 40% sugar, so in 1 quart of this solution:
  \[
  \text{Amount of sugar} = 0.40 \times 1 = 0.4 \text{ quarts of sugar}
  \]

- The 82% solution contains 82% sugar, so in 6 quarts of this solution:
  \[
  \text{Amount of sugar} = 0.82 \times 6 = 4.92 \text{ quarts of sugar}
  \]

### Step 2: Calculate the total amount of sugar in the mixture
Now, add the amounts of sugar from both solutions:
\[
\text{Total sugar} = 0.4 + 4.92 = 5.32 \text{ quarts of sugar}
\]

### Step 3: Calculate the total volume of the mixture
\[
\text{Total volume} = 1 + 6 = 7 \text{ quarts}
\]

### Step 4: Calculate the concentration of the new mixture
The concentration is the total amount of sugar divided by the total volume:
\[
\text{Concentration} = \frac{5.32}{7} \approx 0.76 \text{ or } 76\%
\]

Thus, the concentration of the new mixture is **76%**.

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Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the concentration change if the volumes were reversed?
2. What if you mixed a 50% solution with an 82% solution in equal quantities?
3. How would the concentration change if you mixed 10 quarts of a 20% solution with 5 quarts of an 80% solution?
4. What is the concentration of a mixture when combining 2 quarts of 100% sugar with 5 quarts of 60% sugar?
5. How can you derive a formula for the concentration when mixing any two solutions?

**Tip:** To find the concentration of a mixture, always remember to calculate the total amount of solute first, then divide it by the total volume.

1 qt of a 40% sugar solution was mixed with 6 qt of an 82% sugar solution. Find the concentration of the new mixture.

Learn how to find the concentration of a sugar mixture when combining 1 qt of a 40% sugar solution with 6 qt of an 82% sugar solution. This detailed solution includes calculating total sugar, total volume, and the final concentration. Suitable for students in Grades 8-10.

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