Last year, Carmen had
$20,000
to invest. She invested some of it in an account that paid
9%
simple interest per year, and she invested the rest in an account that paid
5%
simple interest per year. After one year, she received a total of
$1680
in interest. How much did she invest in each account?
.09x + .05(20000-x) = 1680
To find out how much Carmen invested in each account, we can set up a system of equations. Let's say she invested x dollars in the account that paid 9% interest, and y dollars in the account that paid 5% interest.
The equation for the first account would be: 0.09x (since 9% is equivalent to 0.09 in decimal form).
The equation for the second account would be: 0.05y (since 5% is equivalent to 0.05 in decimal form).
According to the information given, the total interest earned is $1680. So, we can set up our equation as follows:
0.09x + 0.05y = 1680
We also know that Carmen invested a total of $20,000 in both accounts, so we can set up another equation:
x + y = 20000
Now we have a system of two equations:
0.09x + 0.05y = 1680
x + y = 20000
We can solve this system of equations using substitution or elimination method to find the values of x and y, representing the amounts invested in each account.