Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest,

Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the total interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent

$800 in account that pays 10% interest $2,200 in account that pays 8% interest Explanation: Account A = Money market account that paid 10% simple annual interest Account B = Money market account that paid 8% simple annual interest W1 = Proportion of money invested in Account A W2 = Proportion of money invested in Account B W1 + W2 = 1 therefore, W1 = 1 – W2 Principle amount = $3,000 3000 x W1 = Amount of money invested in Account A 3000 x W2 = Amount of money invested in Account B Total interest earned = $256 R1 = 10% simple interest on Account A R2 = 8% simple interest on Account B) Total Interest = (Principle x W1 x R1) + (Principle x W2 x R2) 256 = (3000 x W1 x 10%) + (3000 x W2 x 8%) 256 = 300 W1 + 240 W2 256 = 300 W1 + 240 ( 1 – W1) 256 = 300 W1 + 240 – 240 W1 16 = 60 W1 W1 = 16 / 60 W2 = 1 – W1 = 1 – (16/60) = 11/15 Amount of money invested in Account A = 3000 x W1 = 3000 x (16/60) = $800 Amount of money invested in Account B = 3000 x W2 = 3000 x (11/15) =$2,200

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how much did Pat invest at 10 percent and how much at 8 percent? 2200 10%  800  8% Explanation: I=C*%I*T
I=C1*0,08*1+C2*0,10*1
3000=C1+C2
C1=3000-C2
256=(3000-C2)*0,08+C2*0,10
256=240-0,08C2+O,10C2
16=0,02C2
C2=800
C1=2200
I=2200*0,1= 176
I=800*0,08=80

4900 Step-by-step explanation:

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