Kendra invested twice as much money at an annual rate of 7% as she did at an annual rate of 5.5%. How much did she invest at the higher rate if her income from these investments for one year totaled $175.50?

$1,679.42

Step-by-step explanation:

Let be the amount Kendra invested at 5.5%. Since the amount invested at 7% is twice the amount she invested at 5.5%, she invested at 7%.

Remember that , where:

is the interest earned

is the principal or initial investment

is the interest rate in decimal form

is the time in years

- For the 5.5% investment:

Let's replace the values in our formula, , which simplified is

- For the 7% investment:

Now, we that the the amount of interest earned combining the two investment is $175.50, so:

She invested $839.71 at 5.5%, and since she invested twice that amount at 7%, she invested 2*($839.71 ) = $1,679.42 at 7% (the higher rate).