Pregunta
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
Solución de tutoría real
Respuesta verificada por el tutor
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The number is 20.
Solución
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
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución 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 \( B) 20 \).
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