Question
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
Ask by Klein Cook. in China
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number is 20.
Solution
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
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To solve for the unknown number using the given ratio, we first convert the mixed numbers into improper fractions. The mixed number \( 1 \frac{3}{4} \) converts to: \[ 1 \frac{3}{4} = \frac{4 \cdot 1 + 3}{4} = \frac{7}{4} \] The mixed number \( 2 \frac{1}{2} \) converts to: \[ 2 \frac{1}{2} = \frac{2 \cdot 2 + 1}{2} = \frac{5}{2} \] Next, we form the ratio: \[ \frac{1 \frac{3}{4}}{2 \frac{1}{2}} = \frac{\frac{7}{4}}{\frac{5}{2}} = \frac{7}{4} \cdot \frac{2}{5} = \frac{14}{20} \] Now, we set up the given condition: \[ \frac{14}{20} = \frac{14}{x} \] Cross-multiplying gives us: \[ 14x = 14 \cdot 20 \] This simplifies to: \[ x = 20 \] So, the answer is \( B) 20 \).
