Question

Quick Fix Inc. repairs bikes. Their revenue, in dollars, can be modeled by the equation y = 400 + 220x, where x is the number of hours spent repairing bikes. Their overhead cost, in dollars, can be modeled by the equation y=20x^2+160 , where x is the number of hours spent repairing bikes.

After how many hours does the company break even?

Note: The phrase break even refers to the value where the two functions are equivalent

Answer 1

Im thinking 30

Answer 2

@dude

Answer 3

3,760 overhead cost if x=30

Answer 4

7k revenue x=30

Answer 5

Just set them equal to each other and solve for x
\(400+220x=20x^2+160\)

Answer 6

x=0?

Answer 7

set them to x =0

Answer 8

No no, just isolate x

Answer 9

OH

Answer 10

i see what you did

Answer 11

400=20x^2-60

Answer 12

400=20x-60
460=20x

Answer 13

23=x

Answer 14

Step 1: \(400+220x=20x^2+160\)
Step 2: \(400+220x\color{red}{-400}=20x^2+160\color{red}{-400}\)
Step 3: \(220x\color{red}{-220x}=20x^2-240\color{red}{-220x}\)
Solve: \(0=20x^2-220x-240\)
From here we can use the quadratic formula

Answer 15

uhhhhh

Answer 16

I kinda maybe sorta didnt learn the formula ._.

Answer 17

You don't have to use it

Answer 18

Every number in the equation is divisible by 20, so just simplify and then factor like you normally would

Answer 19

20+11x=x^2+8

Answer 20

Ok so now you need to put everything on one side. Basically make it look like a normal quadratic equation

Answer 21

y=x^2+11x+28

Answer 22

?

Answer 23

One sec let me write it out

Answer 24

cant you just type it? no offense. But i could read it easier

Answer 25

I can try lol
20+11x=x^2+8
-20 -11x
x^2-11x-12=0

Answer 26

and i can just solve it?

Answer 27

Oh it is 12 ;o

Answer 28

Thanks :D

Answer 29

Np :)