The ratio of $$ 1 \frac{3}{4} $$ to $$ 2 \frac{1}{2} $$ is equal to the ratio of 14 to what number? A) 18 B) 20 C) 22 D) 24

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To solve the problem, we need to find the number $$ x $$ such that the ratio of $$ 1 \frac{3}{4} $$ to $$ 2 \frac{1}{2} $$ is equal to the ratio of 14 to $$ x $$.

1. **Convert Mixed Numbers to Improper Fractions:**
   $$
   1 \frac{3}{4} = \frac{7}{4} \quad \text{and} \quad 2 \frac{1}{2} = \frac{5}{2}
   $$

2. **Set Up the Ratio Equation:**
   $$
   \frac{\frac{7}{4}}{\frac{5}{2}} = \frac{14}{x}
   $$

3. **Simplify the Left Side:**
   $$
   \frac{7}{4} \div \frac{5}{2} = \frac{7}{4} \times \frac{2}{5} = \frac{14}{20} = \frac{7}{10}
   $$

4. **Set Up the Proportion:**
   $$
   \frac{7}{10} = \frac{14}{x}
   $$

5. **Solve for $$ x $$:**
   $$
   7x = 140 \quad \Rightarrow \quad x = 20
   $$

**Answer:** B) 20
The number is 20.

The ratio of to is equal to the ratio of 14
to what number?
A) 18
B) 20
C) 22
D) 24

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The ratio of to is equal to the ratio of 14 to what number? A) 18 B) 20 C) 22 D) 24