Question
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
Real Tutor Solution
Tutor-Verified Answer
Answer
The unknown "?" is \( \frac{40}{3} \) or \( 13\frac{1}{3} \).
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution 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.
