Question 189683
Let 

x=amount of money that the elder son receives and 

y=amount of money that the younger son receives 



Because $3000 is being split among the two, this means that {{{x+y=3000}}} (ie if you add their shares together, you will get $3000)


Also, since "$3000 are divided between two sons so that the elder son receives $200 more than two-thirds the share of the younger son", this tells us that {{{x=(2/3)y+200}}}



{{{x+y=3000}}} Start with the first equation.
 


{{{(2/3)y+200+y=3000}}} Plug in {{{x=(2/3)y+200}}}



{{{cross(3)((2/cross(3))y)+3(200)+3(y)=3(3000)}}} Multiply EVERY term by the LCD {{{3}}} to clear the fractions.



{{{2y+600+3y=9000}}} Multiply.



{{{5y+600=9000}}} Combine like terms on the left side.



{{{5y=9000-600}}} Subtract {{{600}}} from both sides.



{{{5y=8400}}} Combine like terms on the right side.



{{{y=(8400)/(5)}}} Divide both sides by {{{5}}} to isolate {{{y}}}.



{{{y=1680}}} Reduce.



So this means that the younger son received $1,680



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{{{x=(2/3)y+200}}} Go back to the second equation



{{{x=(2/3)(1680)+200}}} Plug in {{{y=1680}}}



{{{x=3360/3+200}}} Multiply



{{{x=1120+200}}} Reduce



{{{x=1320}}} Combine like terms.




So the elder son received $1,320