Answer:
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
