Question

John gave his son mike 5z number of coins in addition to what he already has. mike then has (y + 10) times as many coins as he had originally. in terms of y and z, how many coins did mike have originally? explanation

Answer 1

Let X be the number of coin Mike has originally. 
Hi father gave him 5z got so he will have now: $X+5z$.
The sentence "mike then has (y + 10) times as many coins as he had originally"
can be written in math form like this:
$X+5z=(y+10)X$
We will solve the above equation for X like this:
$X+5z=(y+10)X\\X-(y+10)X=-5z\\X(1-(y+10))=-5z\\X(-y-9)=-5z\\X=\dfrac{-5z}{-y-9}$
Mike has originally $\dfrac{5z}{y+9}$ coins.