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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 + 5x + 12. The second
friend's profit can be determined by the function Q(x) = 6x. 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.

Respuesta :

linandrew41

To find when they will earn the same profit: we must set the equation of their profits equal:

          [tex]-x^{2} +5x +12 = 6x\\-x^{2} -x+12 = 0\\x^2+x-12 = 0\\(x+4)(x-3) = 0[/tex]

To find the solution of the day when the earned the same profit: we must set (x + 4) = 0  and (x -3) = 0

            we get x = -4 and x = 3

Thus after three days, both students will earn the same profit, the other solution is nonviable because one cannot work negative 4 days.

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