An owner of a key rings manufacturing company found that the profit earned (in thousands of dollars) per day by selling n number of key rings is given by , where n is the number of key rings in thousands. Find the number of key rings sold on a particular day when the total profit is $5,000.n^2-2n-3

Answer:The number of key rings sold on that day is 4000 key ringsStep-by-step explanation:* Lets explain the information in the problem- The profit earned (in thousands of dollars) per day by selling n number   of key rings is given by the function P(n) = n² - 2n - 3, where n is the   number of key rings in thousands and P is the profit in thousands   for one day- On a particular day the total profit is $5,000 ∵ 5000 = 5 in thousands∵ The function P(n) is the profit of n key ring in thousands∴ P(n) = 5- Lets solve the function to find the number of key rings∵ P(n) = n² - 2n - 3∴ 5 = n² - 2n - 3 ⇒ subtract 5 from both sides∴ 0 = n² - 2n - 8 ⇒ factorize it∵ n² = n × n ⇒ 1st terms in the 2 brackets∵ -8 = -4 × 2 ⇒ 2nd terms in the 2 brackets∵ n × -4 = -4n ⇒ nears∵ n × 2 = 2n ⇒ extremes∵ -4n + 2n = -2n ⇒ the middle term∴ (n - 4)(n + 2) = 0 ⇒ equate each bracket by 0 to find n∴ n - 4 = 0 ⇒ add 4 to both sides∴ n = 4 key ring in thousands = 4000 key rings- OR∴ n + 2 = 0 ⇒ subtract 2 from both sides∴ n = -2 ⇒ we will refused this value because number of key rings    must be positive∴ The number of key rings sold on that day is 4000 key rings