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 + 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 1

the question is "After how many days will the two students earn the same profit?" and you're given both profit equations. set them equal to each other and solve for x.

12x = −x^2 + 9x + 10

you'll get 2 solutions, one of them is "nonviable" because x represents number of days which can only be positive/0. the nonviable one will most likely be negative which doesn't make any sense in this context.

Answer 2

okay makes sense but... im assuming to solve the equation you need to Rearrange the equation

Answer 3

and then factor by spliting the middle term

Answer 4

or am i off

Answer 5

12x = −x^2 + 9x + 10

subtract 12x from both sides

-x^2 -3x + 10 = 0

factor or use the quadratic formula

Answer 6

I got 5,-2

Answer 7

hm wait just sec

Answer 8

did i do something wrong

Answer 9

oh damn

Answer 10

i caught myself

Answer 11

-5, 2

Answer 12

yeah, -5,2 that's right, there was probably a sign error somewhere

Answer 13

yep

Answer 14

one little mistake

Answer 15

so how can i make this answer make sense

Answer 16

anyway, plugging these x-values back into Q(x) = 12x gives us (-5,-60) and (2,24) as our solutions

since x = number of days, and y = profits, it doesn't make sense for these to be negative, so we would say (2,24) is our viable solution and (-5,-60) is nonviable. they'll earn the same profit of $24 after 2 days.

Answer 17

makes sense thanksss