I'm having a problem with this number and digits problem. What to do? During the last election , the total number of votes recorded in the municipality of San Juan was 8600. Had one-third of Estrada’s supporters stayed away from the polls and one-half of Arroyo’s behaved likewise , Estrada’s majority would have been reduced by 200.


*

*How many votes did Estrada actually  received?

*How many votes  did Arroyo actually received?

*Determine Estrada’s new majority over Arroyo when both their supporters stayed away from the polls.

 A: Let E = number of Estrada supporters
Let A = number of Arrayo supporters  
Then E + A = 8600 
Estrada's majority -- we don't know what it is yet -- is E - A 
In the second scenario, 1/3 of Estrada's stay home, so he gets 2/3 E votes.
Likewise, 1/2 of Arrayo's fans are at home watching Dr. Who, so he's left with 1/2 A votes.
The new spread, still a majority for Estrada is this: 2/3 E - 1/2 A 
We don't know what Estrado's majority is here, either. But we do know it's decreased by 200:
E - A - 200 = 2/3 E - 1/2 A 
Group like terms and simplify:  
200 = 1/3 E - 1/2 A 
Now we have 2 equations in two unknowns:
200 = 1/3 E - 1/2 A
8600 = E + A 
Can you solve a system of two equations and two unknowns?  Doing so will provide you with values for E and A which you should then go back and plug into the other equations to see if they give the predicted values.
A: HINT
Let $E$ denote the number of voters from Estrada and $A$ - from Arrayo. Then, the total is $A+E = 8600$. Translate the second sentence into an equation and solve them together.
