Sally Finkelstein has a recipe that calls for horseradish sauce that is $$ 65 \% $$ pure horseradish. At the grocery store she finds one horseradish sauce that is $$ 30 \% $$ pure horseradish and another that is $$ 80 \% $$ pure horseradish. How many teaspoons of each of these horseradish sauces should Sally mix together to get 8 teaspoons of horseradish sauce that is $$ 65 \% $$ pure horseradish? The number of teaspoons of $$ 30 \% $$ pure horseradish sauce is (Type an integer or a decimal.)

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To determine how many teaspoons of the $$ 30\% $$ pure horseradish sauce Sally should use, let's set up the problem step-by-step.

**Let:**
- $$ x $$ = teaspoons of $$ 30\% $$ pure horseradish sauce
- $$ 8 - x $$ = teaspoons of $$ 80\% $$ pure horseradish sauce (since the total mixture is 8 teaspoons)

**Total Horseradish Needed:**
Sally wants $$ 8 $$ teaspoons of $$ 65\% $$ pure horseradish sauce:
$$
0.65 \times 8 = 5.2 \text{ teaspoons of pure horseradish}
$$

**Equation Setup:**
The pure horseradish from both sauces should add up to $$ 5.2 $$ teaspoons:
$$
0.30x + 0.80(8 - x) = 5.2
$$

**Solve for $$ x $$:**
$$
0.30x + 6.4 - 0.80x = 5.2
$$
$$
-0.50x + 6.4 = 5.2
$$
$$
-0.50x = -1.2
$$
$$
x = \frac{-1.2}{-0.50} = 2.4
$$

**Conclusion:**
Sally should use **2.4 teaspoons** of the $$ 30\% $$ pure horseradish sauce.

**Answer:**  
2.4
Sally should use 2.4 teaspoons of the 30% pure horseradish sauce.

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