Multiple choice

A certain gadget's manufacturing cost is \$80 to a company. The gadget is sold by a salesperson who earns a commission equal to 15% of the sales price of the gadget. The company's profit for each unit is equal to the sales price minus the sum of the manufacturing cost and the commission. If the sales price of the gadget is \$120, which of the following equations gives the number of units, u, the company must sell to make a total profit of $9,152?

  1. (120(1 - 0.15) - 80)u = 9,152

  2. (120 - 80)(1 - 0.15)u = 9,152

  3. 0.15(120) + 80u = 9,152

  4. 0.85(120) - 80u = 9,152
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A Correct answer
Explanation

Profit per unit = Sales Price - (Manufacturing Cost + Commission). Commission = 0.15 * Sales Price. Profit = 120 - (80 + 0.15 * 120). Total Profit = u * (120 - 80 - 0.15 * 120) = 9152. This simplifies to (120 - 0.15 * 120 - 80)u = 9152, which is (120(1 - 0.15) - 80)u = 9152.

AI explanation

The sales price is \$120 and the commission is 15 percent of the sales price, which is 120 * 0.15. The manufacturing cost is \$80, so the profit per unit is the sales price minus the commission minus the manufacturing cost: 120 - (120 * 0.15) - 80. This simplifies to 120(1 - 0.15) - 80. To find the total profit for u units, this per unit profit is multiplied by u and set equal to $9152.

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