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To solve the equation \(\frac{1}{2} c + 25 = 49\), follow these steps:
1. **Subtract 25 from both sides:**
\[
\frac{1}{2} c + 25 - 25 = 49 - 25
\]
\[
\frac{1}{2} c = 24
\]
2. **Multiply both sides by 2 to isolate \(c\):**
\[
2 \times \frac{1}{2} c = 24 \times 2
\]
\[
c = 48
\]
Thus, the solution for \(c\) is \(c = 48\).