You invested a total of $11,600 in shares of the three stocks at the given prices, and expected to earn $272 in annual dividends. If you purchased a total of 200 shares, how many shares of each stock did you purchase?

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let the number of 3 stocks are x,yz respectively, then we have

x+y+z = 200,

16x+56y+80z = 11600

0.07*16x+0.02*56y+0.02*80z = 272

simplify the equations

x+y+z = 200

x+3.5 y+5z = 725

1.12 x+1.12y+1.6z = 272 or x+y + 10/7 z = 1700/7

x=y=50, z= 100

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