Ann earned a total of $346 in simple interest from two separate accounts. In an account earning 4% interest, Ann invested $1,900 more than three times the amount she invested in an account earning 3%. How much did she invest in each account?

Let total interest earned be #t = $346#

Let the first account be #a_1# at 4% interest rate
Let the second account br #a_2# at 3% interest rate
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#color(brown)("Building the initial equations:")#

In the account earning 4% interest: #" "-> a_1#
..invested $1900 more than:#" " ->a_1=$1900+?#
three times:#" "->a_1=$1900+(3xx?)#

the amount she invested in..3% account
#" "->a_1=$1900+3xxa_2#

Thus before interest we have:

#" "color(green)(a_1=$1900+3a_2)" ".................Equation(1)#

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We are told that the total interest is: #$346 =t#

The contribution to this from both accounts is:

#t=4/100a_1+3/100a_2# giving:

#color(brown)($346=4/100color(green)(a_1)+3/100a_2)" "..................Equation(2)#
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#color(blue)("Determine deposit in account "a_2)#

Substitute for #a_1# in Equation(2) using Equation(1)

#color(brown)($346=4/100(color(green)($1900+3a_2))+3/100a_2)" ".............Equation(2_a)#

#$346=$76+12/100a_2+3/100a_2#

#15/100a_2=$270#

#color(blue)(a_2=$1800)#
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#color(blue)("Determine deposit in account "a_1)#

Using Equation(1)

#a_1=$1900+3a_2" "->" "a_1=$1900+3($1800)#

#color(blue)(a_1= $7300)#