Mary has $65,000 to invest in two accounts. The first account is a private savings offering 6% annual interest and the second account is a government savings account offering 4% annual interest. How much money should Mary invest in each account to make $3520 in total annual interest.

first account with 6% interest ( x ) = $46000

second account with 4% interest ( y ) = $19000

Step-by-step explanation:

Principal = $65000

first interest rate = 6%

second interest rate = 4%

assuming ; X = money invested in first account ,  Y = money invested in second account

hence :

( 65000 - y ) * 6% + ( 65000 - x ) * 4% = 3520

3900 - 0.06 y  + 2600 - 0.04 x = 3520

0.04 x + 0.06 y = 3900 + 2600 - 3520

0.04 x + 0.06 y = 2980 ( 1)

        x + y = 65000   ( 2 )

solve equation 1 and 2 simultaneously by elimination method

0.04 x + 0.06 y = 2980  ( 3 )

0.06 x + 0.06 y = 3900 ( 4 )

subtract equation 3 form equation 4

0.02 x  = 920 ,   hence x = $46000

therefore y = $65000 - $46000 =  $19000

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