Given:
Total invested amount = $5400
Rate of interest for first account = 14%
Rate of interest for second account = 6%
Total interest after one year = $580
To find:
The amount invested in each account.
Solution:
Let the amount invested in the first account be $x, then the amount invested in the second account is $(5400-x).
Total interest = 14% of $x + 6% of $(5400-x).
[tex]580=\dfrac{14}{100}x+\dfrac{6}{100}(5400-x)[/tex]
Multiply both sides by 100.
[tex]58000=14x+6(5400-x)[/tex]
[tex]58000=14x+32400-6x[/tex]
[tex]58000-32400=8x[/tex]
[tex]25600=8x[/tex]
Divide both sides by 8.
[tex]\dfrac{25600}{8}=x[/tex]
[tex]3200=x[/tex]
Now,
[tex]5400-x=5400-3200[/tex]
[tex]5400-x=2200[/tex]
Therefore, the amount invested in first account is $3200 and the amount invested in the second account is $2200.
