https://file.aiquickdraw.com/mathbot/file/1730487774306qoysvnk8.jpg

To solve the given proportion:

\[
\frac{5}{3} = \frac{6}{p + 10}
\]

we can use cross-multiplication. This gives:

\[
5 \cdot (p + 10) = 3 \cdot 6
\]

### Step-by-Step Solution

1. **Expand the left side**:
   \[
   5p + 50 = 18
   \]

2. **Isolate \( p \)** by subtracting 50 from both sides:
   \[
   5p = 18 - 50
   \]
   \[
   5p = -32
   \]

3. **Divide both sides by 5** to solve for \( p \):
   \[
   p = \frac{-32}{5}
   \]

So, the solution is:
\[
p = -\frac{32}{5}
\]

### Final Answer
\[
p = -\frac{32}{5}
\]

Would you like further details or explanations on any step? 

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Here are some related questions to explore further:
1. How do you solve proportions with more complex denominators?
2. How can cross-multiplication be applied in word problems?
3. What are some methods to check if two ratios are equivalent?
4. How do you simplify fractions to their lowest terms?
5. How does this method compare with solving proportions graphically?

**Tip:** Always simplify your final answer if possible; some systems may require it in the simplest form.

Solve the proportion: \(\frac{5}{3} = \frac{6}{p + 10}\)

Learn how to solve the proportion \(\frac{5}{3} = \frac{6}{p + 10}\) using cross-multiplication. This problem covers essential algebraic concepts, including proportions and isolating variables. Suitable for Grade 8 students.

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