\begin{tabular}{l} When hired at a new job selling jewelry, you are given two pay options: \\ Option A: Base salary of \( \$ 18,000 \) a year, with a commission of \( 9 \% \) of your sales \\ Option B: Base salary of \( \$ 22,000 \) a year, with a commission of \( 5 \% \) of your sales \\ In order for option A to produce a larger income, you would need sell at least \( \$ \) \\ \hline\end{tabular}

To determine the sales amount needed for Option A to yield a higher income than Option B, we can set up an inequality. Let \( x \) represent the total sales amount. For Option A, the total income is: \( Income_A = 18,000 + 0.09x \) For Option B, the total income is: \( Income_B = 22,000 + 0.05x \) To find when Option A exceeds Option B: \( 18,000 + 0.09x > 22,000 + 0.05x \) Solving this gives: \( 0.04x > 4,000 \) \( x > 100,000 \) So, you would need to sell at least **\$100,000** for Option A to be more lucrative. To put this into perspective, if you're sitting at a table showcasing beautiful rings or dazzling diamond necklaces, just imagine how many sales you need to hit that mark! If you only sold a couple of items a month, you might be taking home less than that snazzy ring on your finger. So gear up your sales strategies—time to charm those customers! Don't forget that sales records are crucial. Track your sales meticulously to understand your patterns and which jewelry pieces are flying off the shelves. With the right data analytics, you can even predict the best times to ramp up your sales efforts and adjust your strategies for maximum profitability!