A truck can be rented from Company A for $60 a day plus $0.60 per mile . Company B charges $30 a day plus $0.90 per mile to rent the same truck . Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

x = the number of miles

y = the total cost

Company A:

0.60x + 60 = y     [Company A charges $60 plus $0.60 per mile(x)]

Company B:

0.90x + 30 = y      [Company B charges $30 plus $0.90 per mile(x)]

To find the number of miles where the costs for both companies are the same, you can set the equations equal to each other as the costs(y) are the same:

y = y      Substitute the equations into "y" (substitute (0.60x + 60) and (0.90x + 30) into "y" since y = 0.60x + 60 and y = 0.90x + 30)

0.60x + 60 = 0.90x + 30   To find x, isolate/get the variable "x" by itself. Subtract 30 on both sides

0.60x + 60 - 30 = 0.90x + 30 - 30

0.60x + 30 = 0.90x      Subtract 0.60x on both sides to get "x" on one side of the equation

0.60x - 0.60x + 30 = 0.90x - 0.60x

30 = 0.30x      Divide 0.30 on both sides to get "x" by itself

100 = x     100 miles

(if you need to find out the cost where both companies cost the same, you can substitute/plug in the value of x into one of the equations.)

0.60x + 60 = y     Plug in 100 into "x" since x = 100

0.60(100) + 60 = y

120 = y        At 100 miles, both companies cost $120

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb