X • Y = X - Z to get X = Y / (1-Z)

Question

So I was trying to take a formula and start from scratch to recreate it.

So I'm starting with:

X • Y = X - Z

And I'm trying to get it to:

X = Y / (1-Z)

 

if it helps I got on this by thinking about something that equals $11.40 after a 5% discount, what the original price would be.

I know the formula for it is the second one I sent you, so:

X being the original price
X = 11.40/(1-.05)
X= 12

But the I was wondering if I set that up from scratch with the:

X • 0.05 = X - 11.40

How I would solve for X.
And I keep running into problems where I've forgot exactly how to get an X by itself.

I'm stuck at:

2x = -Y / Z

I've probably done something wrong lol, but I couldn't think of what to do next

Answer 1

Thanks for the great explanation of what you did !!    [note: Teachers are forced to give grades; tutors may act as coaches or mentors (on your side) to help you learn.]

 

Let's start at:

    X • 0.05 = X - 11.40 

 

    X - (0.05X) = 11.40                  [you could also start here]

    X(1-0.05) = 11.40

    X = 11.40/(1-0.05)                [the formula]

    X=12

 

In general:

    X • Y = X - Z

    XY = X - Z

    XY - X = -Z                           [subtract X from both sides]

    X - XY = Z                           [multiply both sides by (-1)]

    X(1-Y) = Z                              [alternate starting point]

    X = Z / (1-Y)                           [got there !]

 

 

Now, just asking, how did you get 2X ???