Question

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?

Answer 1

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

`color(red)("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
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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)`

........................................................................................

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)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`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)`