Two friends wash cars to make extra

Answered question

2022-03-22

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 & Explanation

Vasquez

Vasquez

Expert2022-04-28Added 669 answers

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

-x2+9x+10=12x

Move all terms to the left side of the equation and simplify.

Subtract 12x from both sides of the equation.

-x2+9x+10-12x=0

Subtract 12x from 9x.

-x2-3x+10=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=-1b=-3, and c=10 into the quadratic formula and solve for x.

3±(-3)2-4(-110)2-1

Simplify.

x=3±72-1

Multiply 2 by -1.

x=3±7-2

Move the negative in front of the fraction.

x=-3±72

The final answer is the combination of both solutions.

x=5 and x=2

Thus after 2 days, both students will earn the same profit, the other solution is nonviable because one cannot work negative 5 days.

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