# 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?

Nov 26, 2016

color(blue)(a_1 -> 4%" account "= $7300) color(blue)(a_2 -> 3%" account "=$1800)

$\textcolor{red}{\text{The solution demonstrates good communication technique}}$

#### Explanation:

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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ $\textcolor{b r o w n}{\text{Building the initial equations:}}$In the account earning 4% interest: $\text{ } \to {a}_{1}$..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: $\text{ "color(green)(a_1=$1900+3a_2)" } \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left(1\right)$

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We are told that the total interest is: $346 =t The contribution to this from both accounts is: $t = \frac{4}{100} {a}_{1} + \frac{3}{100} {a}_{2}$giving: color(brown)($346=4/100color(green)(a_1)+3/100a_2)" "..................Equation(2)
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$\textcolor{b l u e}{\text{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=$1800)
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$\textcolor{b l u e}{\text{Determine deposit in account } {a}_{1}}$

Using Equation(1)

a_1=$1900+3a_2" "->" "a_1=$1900+3($1800) color(blue)(a_1=$7300)