If the fractions below are equivalent, what are the possible values for $$ x $$ and $$ y $$ ? $$ \begin{array}{l}\frac{16}{36}, \frac{w}{y} \ x=4, y=6 \ x=12, y=32 \ x=20, y=42 \ x=24, y=54\end{array} $$

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UpStudy AI · Accepted Answer

To determine which pairs $$(x, y)$$ make the fractions equivalent to $$\frac{16}{36}$$, follow these steps:

1. **Simplify $$\frac{16}{36}$$:**
   $$
   \frac{16}{36} = \frac{4}{9}
   $$
   So, we're looking for $$(x, y)$$ such that $$\frac{x}{y} = \frac{4}{9}$$.

2. **Check Each Pair:**

- **$$(4, 6)$$:**
     $$
     \frac{4}{6} = \frac{2}{3} \neq \frac{4}{9}
     $$
   - **$$(12, 32)$$:**
     $$
     \frac{12}{32} = \frac{3}{8} \neq \frac{4}{9}
     $$
   - **$$(20, 42)$$:**
     $$
     \frac{20}{42} = \frac{10}{21} \neq \frac{4}{9}
     $$
   - **$$(24, 54)$$:**
     $$
     \frac{24}{54} = \frac{4}{9} = \frac{4}{9}
     $$
     This pair is equivalent.

3. **Conclusion:**
   The only pair that satisfies the condition $$\frac{x}{y} = \frac{4}{9}$$ is $$(24, 54)$$.

**Final Answer:**  
Only when $$x = 24$$ and $$y = 54$$ is the fraction $$\frac{x}{y}$$ equivalent to $$\frac{16}{36}$$.
When $$x = 24$$ and $$y = 54$$, the fractions are equivalent.

If the fractions below are equivalent, what are the possible values for and ?

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