A total of 10,000 is to be divided up between Rita and Miguel, with Miguel to receive 2000 dollar less than Rita. How much will each receive?
$\displaystyle M$ stands for the amount miguel gets.
$\displaystyle R$ stands for the amount rita gets.
You know that: $\displaystyle M+R=10000$
You also know that: $\displaystyle M=R-2000$
Substitute: $\displaystyle (R-2000)+R=10000$
Then: $\displaystyle 2R-2000=10000$
So: $\displaystyle 2R=12000$
Finally: $\displaystyle \boxed{R=6000}$