Question

two friends wash cars to make extra money. The profit P(x) of one friend after x days can be represented by the function P(x)=-x2+9x+10. the second friends profit can be determined by the function Q(x)=12x solve the system of equation. what solution is a variable answer the question, “After how many days will the two students earn the same profit?” and which solution is a nonviable answer? show your work and justify your answer

Answer 1

After solving the system of equations by setting P(x) equals to Q(x), we find that the two friends will earn the same profit after 5 days.

The solution x = -2 is nonviable as the number of days cannot be negative.

Step-by-step explanation:

To find out after how many days the two friends will earn the same profit, we need to solve the system of equations given by the profit functions P(x) and Q(x).

In this case, we set the two functions equal to each other because we want to know when their profits will be the same:

P(x) = Q(x)

-x2 + 9x + 10 = 12x

This simplifies to:

-x2 + 9x + 10 - 12x = 0

-x2 - 3x + 10 = 0

This quadratic equation can be factored as:

-(x - 5)(x + 2) = 0

Which gives us two possible solutions for x:

1. x = 5
2. x = -2

Since the number of days cannot be negative, x = -2 is a nonviable solution.

Therefore, the two friends will earn the same profit after 5 days.