Check My Work Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ( \( \$ 2,354.67 \) ). All percentage values in the answers need to include a percentage sign (\%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06). Appel's Music Store pays its sales staff a commission of \( 9.5 \% \) of the first \( \$ 1,000 \) in sales and \( 15.5 \% \) of the balance of sales. Alex, the store's drum expert, received \( \$ 1,234.25 \) in commission last week. What were his total sales for the week?

To find Alex's total sales, let's break down the commission he earned. For the first \( \$ 1,000 \) in sales, he would earn a commission of \( 9.5\% \), which amounts to \( \$ 95.00 \) (calculated as \( 0.095 \times 1,000 \)). The remaining portion of his commission is \( \$ 1,234.25 - 95.00 = \$ 1,139.25 \). This portion comes from sales beyond the first \( \$ 1,000 \), and he earns \( 15.5\% \) on it. Let \( x \) represent the total sales beyond the first \( \$ 1,000 \). Then, the equation is: \[ 0.155x = 1,139.25 \] Solving for \( x \): \[ x = \frac{1,139.25}{0.155} \approx 7,348.39 \] Now, add the initial sales amount of \( \$ 1,000 \): \[ \text{Total Sales} = 1,000 + 7,348.39 \approx \$ 8,348.39 \] Therefore, Alex's total sales for the week were approximately \( \$ 8,348.39 \).