Aretailer that n games can be sold in a month at a price of 20-0.1n dollars per game. Assume that he buys each game for $13, and sells every one that he buys. if he whishes to make a profit of at least $100 per month on sales of this game, how many games must he sell each month?
A) $$0 \leq n \leq 20$$
B) $$20 \leq n \leq 50$$
C) $$20 \leq n \leq 70$$
D) $$25 \leq n \leq 35$$

Question

Quizplus · Accepted Answer

To find the number of games (n) the retailer must sell to make at least $100 profit, we first determine the profit per game, then find the total profit, and solve for n. The selling price per game is $20-0.1n, and the cost is $13, so the profit per game is $(20-0.1n) - $13 = $7-0.1n. The total profit for n games is n($7-0.1n). Setting this equal to $100 (the minimum desired profit) gives us the equation n($7-0.1n) = $100. Simplifying, we get $7n - 0.1n^2 = $100. Rearranging, we get $0.1n^2 - 7n + 100 = 0. Solving this quadratic equation for n gives us the range of n that satisfies the profit requirement. The correct range that meets the condition for a profit of at least $100 is 20 ≤ n ≤ 50.

Aretailer That N Games Can Be Sold in a Month 0≤n≤200 \leq n \leq 200≤n≤20

Aretailer That N Games Can Be Sold in a Month $0 \leq n \leq 20$