Pregunta
Wilglory writes \( \frac{?}{30}=\frac{200}{450} \). Camerori writes \( \frac{30}{450}=\frac{?}{200} \). a. Both students get the same solution when they solve their equations. What is it?
Ask by Gough O'Quinn. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The unknown "?" is \( \frac{40}{3} \) or \( 13\frac{1}{3} \).
Solución
To solve for the unknown "?" in both equations provided by Wilglory and Camerori, let's break down each equation step by step.
### Wilglory's Equation:
\[ \frac{?}{30} = \frac{200}{450} \]
**Step 1: Simplify the Fraction \(\frac{200}{450}\)**
\[
\frac{200}{450} = \frac{20}{45} = \frac{4}{9}
\]
**Step 2: Solve for "?"**
\[
\frac{?}{30} = \frac{4}{9} \\
? = 30 \times \frac{4}{9} \\
? = \frac{120}{9} \\
? = \frac{40}{3} \quad \text{or} \quad 13\frac{1}{3}
\]
### Camerori's Equation:
\[ \frac{30}{450} = \frac{?}{200} \]
**Step 1: Simplify the Fraction \(\frac{30}{450}\)**
\[
\frac{30}{450} = \frac{1}{15}
\]
**Step 2: Solve for "?"**
\[
\frac{1}{15} = \frac{?}{200} \\
? = 200 \times \frac{1}{15} \\
? = \frac{200}{15} \\
? = \frac{40}{3} \quad \text{or} \quad 13\frac{1}{3}
\]
### Conclusion:
Both students arrive at the same solution for "?", which is:
\[
? = \frac{40}{3} \quad \text{or} \quad 13\frac{1}{3}
\]
**Answer:** Both solutions equal 40⁄3, that is, the unknown “?” is 40/3.
Revisado y aprobado por el equipo de tutoría de UpStudy
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Bonus Knowledge
To find the solution for Wilglory's equation \( \frac{?}{30}=\frac{200}{450} \), we can cross-multiply: \[ ? \cdot 450 = 200 \cdot 30 \] \[ ? \cdot 450 = 6000 \] \[ ? = \frac{6000}{450} = \frac{600}{45} = \frac{40}{3} \approx 13.33 \] Now for Camerori's equation \( \frac{30}{450}=\frac{?}{200} \), we again cross-multiply: \[ 30 \cdot 200 = 450 \cdot ? \] \[ 6000 = 450 \cdot ? \] \[ ? = \frac{6000}{450} = \frac{600}{45} = \frac{40}{3} \approx 13.33 \] Both students find that \( ? \) is \( \frac{40}{3} \) or approximately 13.33.
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