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

The number of key rings sold on that day is 4000 key rings

Step-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