# SOLUTION: A person invests \$50,000 for one year; some is invested at 7%, some at 8%, and the remainder at 12%. The combined interest earned at the end of the year from these investments was

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 Question 525995: A person invests \$50,000 for one year; some is invested at 7%, some at 8%, and the remainder at 12%. The combined interest earned at the end of the year from these investments was \$4,770. the amount invested at 8% is \$4000 more then the amount invested at 7% and 12% combined. find the amount of money invested at each rateAnswer by mananth(12270)   (Show Source): You can put this solution on YOUR website!7%--------------x 8%--------------(x+y+4000) 12%-------------y x+x+y+4000+y= 50000 2x+2y+4000=50000 2x+2y=46000 /2 x+y=23000..............(1) 7x+8(x+y+4000)+12y= 4770 *100 ( the % is converted by multiplying by 100) 7x+8x+8y+32000+12y=477000 15x+20y=477000-32000 15x+20y=445000 /5 3x+4y=89000................(2) 1 x + 1 y = 23000 .............1 3 x + 4 y = 89000 .............2 Eliminate y multiply (1)by -4 Multiply (2) by 1 -4 x -4 y = -92000 3 x 4 y = 89000 Add the two equations -1 x = -3000 / -1 x = 3,000.00 plug value of x in (1) 1 x + 1 y = 23000 3000 + 1 y = 23000 1 y = 23000 -3000 7%--------------x= \$3,000 8%--------------(x+y+4000)= \$27000 12%-------------y= 20000 m.ananth@hotmail.ca