Question
\( \frac{p-2 q}{2 p+q}=\frac{2}{5} \) find the ratio \( p: q \)
Ask by Deleon Fitzgerald. in Sierra Leone
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The ratio \( p : q \) is \( 12 : 1 \).
Solution
To find the ratio \( p : q \) given the equation:
\[
\frac{p - 2q}{2p + q} = \frac{2}{5}
\]
Let's solve for \( p \) in terms of \( q \).
1. **Cross-Multiply:**
\[
5(p - 2q) = 2(2p + q)
\]
2. **Expand Both Sides:**
\[
5p - 10q = 4p + 2q
\]
3. **Group Like Terms:**
\[
5p - 4p = 2q + 10q
\]
\[
p = 12q
\]
4. **Express the Ratio \( p : q \):**
\[
p : q = 12q : q = 12 : 1
\]
**Final Answer:**
The ratio \( p : q \) is \( 12 : 1 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To solve the equation \( \frac{p-2q}{2p+q}=\frac{2}{5} \), we can cross-multiply: \[ 5(p - 2q) = 2(2p + q) \] Expanding both sides gives us: \[ 5p - 10q = 4p + 2q \] Now, we rearrange the equation to isolate terms involving \( p \) and \( q \): \[ 5p - 4p = 10q + 2q \] This simplifies to: \[ p = 12q \] To find the ratio of \( p \) to \( q \), we can express it as: \[ \frac{p}{q} = 12 \] Thus, the ratio \( p : q = 12 : 1 \).
