Question
\( \begin{array}{l} \frac{3}{5} r=2 \\ \frac{5}{3} \cdot \frac{\square}{5} r=\square \cdot \frac{5}{3} \\ r=\frac{2}{\square} \cdot \frac{5}{3} \\ r=\frac{10}{3}=\square \\ \text { (Type whole numbers, fractions, or mixed numbers.) }\end{array} \)
Ask by Hammond Martin. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( r = \frac{10}{3} \)
Solution
Sure, let's fill in the missing numbers step by step.
\[
\begin{array}{l}
\frac{3}{5} r = 2 \\
\frac{5}{3} \cdot \frac{\boxed{3}}{5} r = \boxed{2} \cdot \frac{5}{3} \\
r = \frac{2}{\boxed{1}} \cdot \frac{5}{3} \\
r = \frac{10}{3} = \boxed{\frac{10}{3}} \\
\text{(Type whole numbers, fractions, or mixed numbers.)}
\end{array}
\]
**Filled-in Numbers:**
1. **First Blank in Line 2:** \(3\)
2. **Second Blank in Line 2:** \(2\)
3. **Blank in Line 3:** \(1\)
4. **Blank in Line 4:** \(\frac{10}{3}\)
**Final Solution:**
\[
r = \frac{10}{3}
\]
You can also express \(\frac{10}{3}\) as a mixed number:
\[
r = 3 \frac{1}{3}
\]
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
To solve for \( r \) in the equation \( \frac{3}{5} r = 2 \), we can multiply both sides by \( \frac{5}{3} \) to isolate \( r \). This gives us \( r = 2 \cdot \frac{5}{3} = \frac{10}{3} \). So, the square represents the value \( \frac{10}{3} \), which can also be expressed as the mixed number \( 3 \frac{1}{3} \). Next, in the equation \( r = \frac{2}{\square} \cdot \frac{5}{3} \), substituting \( r = \frac{10}{3} \) leads us to find \( \square \). Rearranging gives \( \square = \frac{2 \cdot 5}{10} = 1 \). So, the second square is \( 1 \).
