Question

400/x - 400/x+12 = 5/3
Find x

Answer 1

Is your question: \(\dfrac{400}{x}-\dfrac{400}{x+12}=\dfrac{5}{3}\) ?

Answer 2

Yes

Answer 3

Find the common denominator between x, x+12 and 3.

Answer 4

That would be \[x(x+12)(3)\]

Answer 5

So now multiply both sides of your equation by \(x(x+12)(3)\)

Answer 6

\[\large x(x+12)(3)\left[ \dfrac{400}{x}-\dfrac{400}{x+12}\right]=\left[\dfrac{5}{3}\right]x(x+12)(3)\]

Answer 7

Distribute \(x(x+12)(3)\) to each term and cancel out the like terms. This ill help you eliminate the denominator for you to solve a linear function.

Answer 8

?

Answer 9

What is \[\frac{400}{x} \cdot x(x+12)(3)=~? \]What cancels out here?

Answer 10

x

Answer 11

400(x+12)(3)?

Answer 12

Great. That is correct.

Answer 13

\[-\frac{400}{x+12} \cdot x(x+12)(3)=~?\]

Answer 14

\[\frac{5}{3}\cdot x(x+12)(3)=~?\]

Answer 15

5x(x+12)(3)?

Answer 16

and 400x(3)

Answer 17

Awesome. Thats correct.

Answer 18

So now you have \[400(x+12)(3) -400(3)(x)=5(x)(x+12)\]

Answer 19

Do you think you can solve it from here?

Answer 20

umm?
can we cancel "x+12" from both sides?

Answer 21

No because it is not a common term on both sides of the equation. \((x+12)\) is not multiplied to \(-400(x)(3)\)

Answer 22

The only time we would be able to cancel something like that out is if we factored it out from the left side of the equation, that is, if it was a common term.

Answer 23

What next?

Answer 24

Just expand the left hand side and the right hand side of the equation and solve for x.

Answer 25

So what do you get for the RHS of the equation first, since that's easier to solve?

Answer 26

5x^2+60x?

Answer 27

Yup.

Answer 28

And \(400(3)(x+12)=~?\)

Answer 29

400(3x + 36)
1200x +14400?

Answer 30

Good.

Answer 31

Putting that altogether, we get \[1200x+14400-1200x=5x^2+60x\]

Answer 32

See anything that cancels out?

Answer 33

1200x

Answer 34

So what does our equation become when 1200x is eliminated?

Answer 35

5x^2 + 60x - 14400 = 0

Answer 36

Good, now divide everything by 5.

Answer 37

What do you get? @AaronAndyson

Answer 38

Sorry I had to wash my hands
I got
x^2 + 12 - 2880 = 0

Answer 39

Awesome, now we get to use the quadratic formula to find our roots, or x values.

Answer 40

So we solve for \[x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\]\[x=\frac{-12\pm\sqrt{(12)^2-4(1)(-2880)}}{2}\]

Answer 41

I'm suppose to factor -_-

Answer 42

nope. What is \((12)^2-4(-2880)=~?\)

Answer 43

They had said that we are suppose to factor

Answer 44

Oh, you can't use the quadratic? Ok.

Answer 45

Well... What are two numbers that multiply to give you -2880 and add to give you 12?

Answer 46

When they specific in the question to use the formula only then we can use it over here they did'nt

Answer 47

ahh. Gotcha.

Answer 48

and 24 , 12?

Answer 49

Does 24 \(\times\) 12 = 2880?

Answer 50

240*

Answer 51

Write out all the factors for 12, and all the factors for 2880.Maybe that will help

Answer 52

Yes, 240 \(\times \) 12 = 2880

Answer 53

But... does 240 -12 = 12?

Answer 54

No

Answer 55

Alright, start at 40, and divide 2880 by 40. what will that give you?

Answer 56

Then take the number produced and subtract it by your factor. This will help you find the middle number

Answer 57

72?

Answer 58

Yes, therefore does 72-40 give you 12?

Answer 59

No

Answer 60

Move up a little bit. you know 2880 ends in a 0 therefore it has to be a number divisible by an even factor....along those lines. So try 42.

Answer 61

68.571

Answer 62

Doesnt work. moving on. 45?

Answer 63

64?

Answer 64

And 64 - 45 = ?

Answer 65

19?

Answer 66

yeah, close right? Moving on.

Answer 67

Lets try another even number. 46?

Answer 68

62.60

Answer 69

Doesnt work. Moving on once again

Answer 70

How about 48?

Answer 71

60
and
60-48 = 12

Answer 72

Woot. there you go.

Answer 73

Now that we've found out factors, lets write our quadratic in factored form.

Answer 74

What would be the factored form with 48 and 60 as our factors?

Answer 75

x = -48 or x = 60

Answer 76

-60 and + 48*

Answer 77

Yep :)

Answer 78

Good job.

Answer 79

Thanks
Can you help me more?

Answer 80

Sorry, its kind of late here and I'm about to head off.

Answer 81

Then,Goodnight.

Answer 82

Good luck

Answer 83

Thanks