A bleach is $$ 5.25 \% $$ sodium hypochlorite and swimming pool shock treatment is $$ 10.5 \% $$ sodium hypochlorite. How much of each item must be mixed to get 6 cups of a mixture that is $$ 7.3 \% $$ sodium hypochlorito? To get 6 cups of a mixture that is $$ 7.3 \% $$ sodium hypochlorite, approximately $$ \square $$ cups of a bleach and approximately $$ \square $$ cups of a swimming pool shock treatment must be mixed. (Round to two decimal places as needed.)

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To determine how much bleach and swimming pool shock treatment to mix to obtain 6 cups of a $$7.3\%$$ sodium hypochlorite solution, follow these steps:

1. **Define Variables:**
   - Let $$ x $$ be the number of cups of bleach ($$5.25\%$$ sodium hypochlorite).
   - Let $$ y $$ be the number of cups of swimming pool shock treatment ($$10.5\%$$ sodium hypochlorite).

2. **Set Up Equations:**
   - **Total Volume Equation:** 
     $$
     x + y = 6
     $$
   - **Sodium Hypochlorite Concentration Equation:** 
     $$
     0.0525x + 0.105y = 0.073 \times 6
     $$
     $$
     0.0525x + 0.105y = 0.438
     $$

3. **Solve the System of Equations:**
   
   From the total volume equation:
   $$
   y = 6 - x
   $$
   
   Substitute $$ y $$ into the concentration equation:
   $$
   0.0525x + 0.105(6 - x) = 0.438
   $$
   $$
   0.0525x + 0.63 - 0.105x = 0.438
   $$
   $$
   -0.0525x + 0.63 = 0.438
   $$
   $$
   -0.0525x = -0.192
   $$
   $$
   x = \frac{0.192}{0.0525} \approx 3.66 \text{ cups}
   $$
   
   Then, find $$ y $$:
   $$
   y = 6 - 3.66 = 2.34 \text{ cups}
   $$

4. **Final Answer:**

To obtain 6 cups of a $$7.3\%$$ sodium hypochlorite mixture, you should mix:

- **Approximately 3.66 cups of bleach**
- **Approximately 2.34 cups of swimming pool shock treatment**

**Rounded to two decimal places:**
- **Bleach:** 3.66 cups
- **Shock Treatment:** 2.34 cups

Answer:
To make 6 cups of 7.3% solution, mix approximately 3.66 cups of bleach with 2.34 cups of shock treatment.
To make 6 cups of a 7.3% sodium hypochlorite mixture, mix approximately 3.66 cups of bleach with 2.34 cups of swimming pool shock treatment.

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