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 + 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 1

According to the profit equations given, it is found that since the number of days has to be a positive value, hence the viable answer is that they earn the same profit after 3 days, while the nonviable answer is -4.

What are the profit equations?

For the first friend, it is:

$P(x) = -x^2 + 5x + 12$

For the second, it is:

$Q(x) = 6x$.

The system we solve to find when they earn the same profit is given by:

$P(x) = Q(x)$

$-x^2 + 5x + 12 = 6x$

$x^2 + x - 12 = 0$

Which is a quadratic equation with coefficients a = 1, b = 1, c = -12. Hence:

$\Delta = b^2 - 4ac = 1^2 - 4(1)(-12) = 49$

$x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-1 + 7}{2} = 3$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-1 - 7}{2} = -4$

The number of days has to be a positive value, hence the viable answer is that they earn the same profit after 3 days, while the nonviable answer is -4.

More can be learned about a system of equations at brainly.com/question/24342899