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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