A golfer has two options for membership in a golf club. A social membership costs $$ \$ 1775 $$ in annual dues. In addition, he would pay a $$ \$ 50 $$ greens fee and a $$ \$ 25 $$ golf cart fee every time he played. A golf membership costs $$ \$ 2425 $$ in annual dues. With this membership, the golfer would only pay a $$ \$ 25 $$ golf cart fee when he played. How many times per year would the golfer need to play golf for the two options to cost the same? The golfer would need to golf

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To determine how many times the golfer needs to play golf for the two membership options to cost the same, let's set up the equations for each option.

**Option 1: Social Membership**
- **Annual Dues:** \$1,775
- **Per Game Cost:** \$50 (greens fee) + \$25 (golf cart fee) = \$75
- **Total Cost:** $$ C_1 = 1,775 + 75x $$

**Option 2: Golf Membership**
- **Annual Dues:** \$2,425
- **Per Game Cost:** \$25 (golf cart fee only)
- **Total Cost:** $$ C_2 = 2,425 + 25x $$

**Setting the Costs Equal:**
$$ 1,775 + 75x = 2,425 + 25x $$

**Solving for $$ x $$:**
$$
\begin{align*}
75x - 25x &= 2,425 - 1,775 \
50x &= 650 \
x &= \frac{650}{50} \
x &= 13
\end{align*}
$$

**Verification:**
- **Option 1:** $$ 1,775 + 75 \times 13 = 1,775 + 975 = \$2,750 $$
- **Option 2:** $$ 2,425 + 25 \times 13 = 2,425 + 325 = \$2,750 $$

Both options cost \$2,750 when the golfer plays 13 times a year.

**Conclusion:**
The golfer would need to golf **13 times per year** for the two membership options to cost the same.

**Answer:**  
The golfer would need to golf **13 times per year** for the two options to cost the same.
The golfer needs to play **13 times per year** for both membership options to cost the same.

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