10. Find the value of $$ x $$ so that the ratios $$ 8: 20 $$ and $$ 6: x $$ are equivalent. Show the process. (Hint rewrite the ratios as fractions, then use cross products to solve).

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To find the value of $$ x $$ that makes the ratios $$ 8:20 $$ and $$ 6:x $$ equivalent, follow these steps:

1. **Rewrite the Ratios as Fractions:**

$$
   \frac{8}{20} = \frac{6}{x}
   $$

2. **Use Cross Multiplication:**

Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction. This gives:

$$
   8 \times x = 20 \times 6
   $$

$$
   8x = 120
   $$

3. **Solve for $$ x $$:**

To isolate $$ x $$, divide both sides of the equation by 8:

$$
   \frac{8x}{8} = \frac{120}{8}
   $$

$$
   x = 15
   $$

4. **Conclusion:**

The value of $$ x $$ that makes the ratios $$ 8:20 $$ and $$ 6:x $$ equivalent is **15**.

**Verification:**

To ensure the ratios are indeed equivalent with $$ x = 15 $$:

$$
\frac{8}{20} = \frac{2 \times 4}{5 \times 4} = \frac{2}{5}
$$

$$
\frac{6}{15} = \frac{2 \times 3}{5 \times 3} = \frac{2}{5}
$$

Both simplified fractions are $$ \frac{2}{5} $$, confirming that the ratios are equivalent when $$ x = 15 $$.
$$ x = 15 $$

10. Find the value of \( x \) so that the ratios \( 8: 20 \) and \( 6: x \) are equivalent. Show the process. (Hint rewrite the ratios as fractions, then use cross products to solve).

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