A profit, P(X), for a certain item is a function relating the income from sales,S(X), and the cost of the item,C(X), The function is stated by the equation shown, where x is the number of items sold.
P(X) = S(X) - C(X)
When S(X) = 0.5x and C(X) = 10 + 0.1x, the range of P(X) contains the elements {350,470,590}. Which set of elements represents the corresponding domain?
A) {130,178,226}
B) {200,272,290}
C) {600,800,1000}
D) {900,1200,1500}
P(x) = .4x-10
so, P(x)=350 when x=900
Looks like D is the likely answer
To find the corresponding domain for the given range of P(X) = {350, 470, 590}, you need to substitute these values into the profit equation P(X) = S(X) - C(X) and solve for the corresponding values of X.
Given:
S(X) = 0.5x
C(X) = 10 + 0.1x
Substitute each value of P(X) into the profit equation:
350 = 0.5x - (10 + 0.1x)
470 = 0.5x - (10 + 0.1x)
590 = 0.5x - (10 + 0.1x)
Simplify each equation:
350 = 0.4x - 10
470 = 0.4x - 10
590 = 0.4x - 10
Add 10 to both sides of each equation:
360 = 0.4x
480 = 0.4x
600 = 0.4x
Divide both sides of each equation by 0.4:
x = 900
x = 1200
x = 1500
The corresponding values of X are 900, 1200, and 1500. Therefore, the set of elements that represents the corresponding domain is:
D) {900, 1200, 1500}