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.

Answer:$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: [tex]a[/tex] the amount invested in the high-risk venture fund and [tex]b[/tex], the amount invested in the mutual fund and we know that the sum of [tex]a[/tex] and [tex]b[/tex] is $30,000.The amount earned ($2,790) can be expressed in the following equation:[tex]0.115a+0.06b=2790[/tex], where [tex]a[/tex] is multiplied by 11.5% and b is multiplied by 6% Since we know that the sum of [tex]a[/tex] and [tex]b[/tex] is $30,000, we can rearrange that equation to solve for [tex]a[/tex], as follows:[tex]a = 30000-b[/tex]We can now replace [tex]a[/tex] in the earlier equation to obtain an expression with only one unknown value:[tex]0.115(30000-b) + 0.06b = 2790[/tex]Which can be rearranged and solved for [tex]b[/tex]:[tex]3450 - 0.115b + 0.06b = 2790\\b = 12000[/tex]Now, using the fact that [tex]a+b=30000[/tex] we can find [tex]a[/tex]:[tex]a=30000-b=30000-12000=18000[/tex]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%