1.2 Homework Question 7, 1.2.63 , How many ounces of a $$ 15 \% $$ alcohol solution must be mixed with 13 ounces of a $$ 20 \% $$ alcohol solution to make a $$ 16 \% $$ alcohol solution? 0 of $$ 1 \leftarrow $$ Po.

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To determine how many ounces of a **15%** alcohol solution need to be mixed with **13 ounces** of a **20%** alcohol solution to obtain a **16%** alcohol solution, let's set up the equation based on the concentration of alcohol in each solution.

**Let $$ x $$ be the number of ounces of the 15% solution needed.**

1. **Calculate the amount of pure alcohol in each solution:**
   - **15% solution:** $$ 0.15x $$ ounces of alcohol
   - **20% solution:** $$ 0.20 \times 13 = 2.6 $$ ounces of alcohol

2. **Total volume and desired concentration:**
   - **Total volume:** $$ x + 13 $$ ounces
   - **Desired alcohol concentration:** 16%, so total pure alcohol needed is $$ 0.16(x + 13) $$ ounces

3. **Set up the equation:**
   $$
   0.15x + 2.6 = 0.16(x + 13)
   $$

4. **Solve for $$ x $$:**
   $$
   0.15x + 2.6 = 0.16x + 2.08
   $$
   $$
   2.6 - 2.08 = 0.16x - 0.15x
   $$
   $$
   0.52 = 0.01x
   $$
   $$
   x = \frac{0.52}{0.01} = 52
   $$

**Conclusion:**
You need to mix **52 ounces** of the **15%** alcohol solution with **13 ounces** of the **20%** alcohol solution to obtain a **16%** alcohol solution.

**Answer:** 52 ounces of the 15 % alcohol solution are needed.
You need to mix 52 ounces of the 15% alcohol solution with 13 ounces of the 20% alcohol solution to get a 16% alcohol solution.

1.2 Homework Question 7, 1.2.63 , How many ounces of a \( 15 \% \) alcohol solution must be mixed with 13 ounces of a \( 20 \% \) alcohol solution to make a \( 16 \% \) alcohol solution? 0 of \( 1 \leftarrow \) Po.

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