If a ring costs a jeweler $$ \$ 1400 $$, at what price should it be sold to yield a profit of $$ 50 \% $$ on the selling price? \$ $$ \square $$

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To determine the selling price that yields a **50% profit on the selling price**, let's break down the problem:

1. **Definitions:**
   - **Cost Price (C):** \$1,400
   - **Selling Price (S):** The price we need to find.
   - **Profit (P):** $$ S - C $$

2. **Understanding the Profit Percentage:**
   - A **50% profit on the selling price** means:
     $$
     P = 0.5 \times S
     $$
   - Substituting the profit definition:
     $$
     S - C = 0.5 \times S
     $$
     $$
     S - 1,400 = 0.5S
     $$

3. **Solving for $$ S $$:**
   $$
   S - 0.5S = 1,400
   $$
   $$
   0.5S = 1,400
   $$
   $$
   S = \frac{1,400}{0.5} = 2,800
   $$

4. **Verification:**
   - **Profit:** $$ 2,800 - 1,400 = 1,400 $$
   - **Profit Percentage on Selling Price:** $$ \frac{1,400}{2,800} \times 100\% = 50\% $$

**Final Answer:** The ring should be sold for **\$2,800** to achieve a 50% profit on the selling price.

**Answer:** $\boxed{2800}$
The ring should be sold for \$2,800 to achieve a 50% profit on the selling price.

If a ring costs a jeweler \( \$ 1400 \), at what price should it be sold to yield a profit of \( 50 \% \) on the selling price? \$ \( \square \)

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