Question 1188040
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x         = invested at 3%;

(x+1000)  = invested at 5%;

the rest,  (16000-x-(x+1000)) = 15000-2x invested at 6%.


The total 1-year interest 


    0.03x + 0.05(x+1000) + 0.06(15000-2x) = 900.


Simplify and find x


    0.03x + 0.05x + 50 + 900 - 0.12x = 900


    0.03x + 0.05x - 0.12x = 900 - 50 - 900


           -0.04x         = -50


              x           = {{{(-50)/(-0.04)}}} = 1250  dollars.


<U>ANSWER</U>.  $1250 invested  at 3%;  $2250 invested at 5%;  and the rest, 16000-1250-2250 = 12500 invested at 6%.


<U>CHECK</U>.  0.03*1250 + 0.05*2250 + 0.06*12500 = 900 dollars, the total annual interest.  ! Precisely correct !
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Solved.