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 friend's 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.

Answer 1

It will take the students 2 days to earn the same profit and the non-viable answer is -5 since it is a negative value

Functions and values

Functions are written as a function of unknown variables

Given the following functions

P(x) = −x² + 9x + 10

Q(x) = 12x

If the student earns the same profit, then;

P(x) = Q(x)

−x² + 9x + 10 = 12x

−x² + 9x + 10 - 12x = 0
x²+3x-10 = 0

Factorize

x²+5x - 2x - 10 = 0
x(x+5)-2(x+5) = 0
x = 2 and -5

It will take the students 2 days to earn the same profit and the non-viable answer is -5 since it is a negative value

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