Two friends wash cars to make extra money.

Answered question

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.

Answer & Explanation

nick1337

nick1337

Expert2022-05-18Added 777 answers

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

 

-x2+5x+12=6x -x2-x+12=0 x2+x-12=0 (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.


 

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?