Explanation:
Let
be the amount invested into the account with a 5% annual interest and
be the amount invested into the account with an 8% annual interest,
It is stated that Helene invested a total of $1000, which can be written mathematically as
.
Subsequently, the total amount of interest after 1 year is $65. This statement can be changed into the equation below.
.
First, divide each term in equation (2) by 0.05, yields the expression
.
Then, let equation (1) be subtracted from equation (3) term-by-term,
.
Therefore, the amount invested in each account is $500.