Suzanne scarpula invested $30,000, part of it in a high risk venture fund that yielded 11.5% per year and the rest in a secure mutual fund paying interest of 6% per year. at the end of one year, suzanne’s investments earned $2,790. find the amount she invested at each rate.

$18,000 was invested in the high-risk venture fund and $12,000 was invested in the mutual fund.

Step-by-step explanation:

In this problem we have two unknowns: the amount invested in the high-risk venture fund and , the amount invested in the mutual fund and we know that the sum of and is $30,000.

The amount earned ($2,790) can be expressed in the following equation:

, where is multiplied by 11.5% and b is multiplied by 6%

Since we know that the sum of and is $30,000, we can rearrange that equation to solve for , as follows:

We can now replace in the earlier equation to obtain an expression with only one unknown value:

Which can be rearranged and solved for :

Now, using the fact that we can find :

Therefore, $18,000 must have been invested in the high-risk venture fund at 11.5% and $12,000 in the mutual fund at 6%

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