How do i solve this ?

[Ap071]

i know the answer but i need a step by step breakdown to understand thank you.

 

[Mr. Bland]

Welcome to Free Math Help!

Rewriting it to make it a bit more manageable:

[MATH]p > 0[/MATH]
[MATH]p \ne r[/MATH]
[MATH] r = \frac{k + p}{k} - 1[/MATH]​

Solve for [MATH]k[/MATH].

Eventually we'll want to get [MATH]k[/MATH] by itself on one side of the equals sign, so each step along the way will involve transforming the equation in such a way that we can get [MATH]k[/MATH] isolated.

We begin by adding 1 to both sides to isolate the fraction:

[MATH]r + 1 = \frac{k + p}{k}[/MATH]​

The fraction can be eliminated by multiplying both sides by [MATH]k[/MATH].

[MATH]k(r + 1) = k + p[/MATH][MATH]rk + k = k + p[/MATH]​

Think you can solve it from here?

 

[Steven G]

I can show you a slightly different method than Mr Bland. This way you can see two different styles.

\(\displaystyle r = \dfrac{k+p}{k} - 1 = \dfrac{k}{k} + \dfrac{p}{k} - 1 = 1+\dfrac{p}{k} - 1 = \dfrac{p}{k}\).

Then k= ??