2022-05-10

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.

nick1337

Expert2022-05-18Added 777 answers

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

$-{x}^{2}+5x+12=6x\phantom{\rule{0ex}{0ex}}-{x}^{2}-x+12=0\phantom{\rule{0ex}{0ex}}{x}^{2}+x-12=0\phantom{\rule{0ex}{0ex}}(x+4)(x-3)=0$

**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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