1 2 3 4 5 6 7 8 9 10 TIME REMAININC 47:56 A company makes a \( \$ 5 \) profit on each non-faulty product it sells. Approximately \( 2 \% \) of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are \( \$ 100 \) each, what is the profit per item? loss of \$15.10 loss of \$15 profit of \( \$ 2.90 \) profit of \( \$ 3.00 \)

To find the profit per item, we need to consider the total profit from selling non-faulty products and the loss from selling faulty products. Given: - Profit on each non-faulty product = $5 - Percentage of faulty products = 2% - Replacement-and-repair cost for faulty products = $100 each Let's assume the total number of products manufactured is \( x \). The number of non-faulty products = \( 0.98x \) (since 2% are faulty) The number of faulty products = \( 0.02x \) Profit from selling non-faulty products = \( 5 \times 0.98x \) Loss from selling faulty products = \( 100 \times 0.02x \) Total profit = Profit from non-faulty products - Loss from faulty products Let's calculate the total profit and then find the profit per item. Simplify the expression by following steps: - step0: Solution: \(5\times 0.98x-100\times 0.02x\) - step1: Multiply the terms: \(4.9x-100\times 0.02x\) - step2: Multiply the terms: \(4.9x-2x\) - step3: Collect like terms: \(\left(4.9-2\right)x\) - step4: Subtract the numbers: \(2.9x\) The total profit is \( 2.9x \). To find the profit per item, we need to divide the total profit by the total number of products manufactured (\( x \)). Profit per item = \( \frac{2.9x}{x} \) Simplifying, we get: Profit per item = \( 2.9 \) Therefore, the profit per item is $2.90.