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) = -x^2 + 9x +10. The second friends profit can be determined by the function Q(x) = 12x. Solve the system of equations. What solution is a viable answer to 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.
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Using a system of equations, it is found that they will have the same profit after 2 days. The solutions x = -5 is non-viable as time measures are non-negative.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

P(x) = -x² + 9x + 10.

Q(x) = 12x.

They have the same profit when:

P(x) = Q(x)

-x² + 9x + 10 = 12x

x² + 3x - 10 = 0

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

x = -5 or x = 2.

They will have the same profit after 2 days. The solutions x = -5 is non-viable as time measures are non-negative.

More can be learned about a system of equations at https://brainly.com/question/24342899