The total revenue R in dollars from selling tops for P dollars each is given by R= P(200-p) where P < or =
200.
Find R when P = $200
Find P when R = $7500
You have posted this question twice -- with a variation.
Which is correct?
http://www.jiskha.com/display.cgi?id=1311885542
the second one is correct
To find the value of R when P = $200, we substitute P = $200 into the equation R = P(200 - P) and solve for R.
1. Start with the given equation: R = P(200 - P).
2. Replace P with $200: R = 200(200 - 200).
3. Simplify: R = 200(0).
4. Evaluate: R = 0.
Therefore, when P = $200, the total revenue R is $0.
To find the value of P when R = $7500, we rearrange the equation R = P(200 - P) and solve for P.
1. Start with the given equation: R = P(200 - P).
2. Rearrange the equation: P^2 - 200P + R = 0.
3. Substitute R = $7500: P^2 - 200P + 7500 = 0.
4. This is now a quadratic equation. We can either solve it by factoring, completing the square, or using the quadratic formula.
Using the quadratic formula:
5. Apply the quadratic formula: P = (-(-200) ± √((-200)^2 - 4(1)(7500))) / (2(1)).
6. Simplify the expression under the square root: P = (200 ± √(40000 - 30000)) / 2.
7. Simplify further: P = (200 ± √10000) / 2.
8. Evaluate: P = (200 ± 100) / 2.
9. Now calculate the two possible values of P:
a. P = (200 + 100) / 2 = 300 / 2 = 150.
b. P = (200 - 100) / 2 = 100 / 2 = 50.
Therefore, when R = $7500, the possible values for P are $150 and $50.