a student invested $10,000 received an inheritance in three parts. with one person she brought mutual funds that offered and returned a 4% per year. the second part which amounted to twice the first was used to buy a government bonds paying 4.5% per year. she put the rest into a savings account that paid 2.5% annual interest. during the first year the total interest was $415. how much did she invest in each rate?​

Answer:The amount invested at 4% per year was $3,000The amount invested at 4.5% per year was $6,000The amount invested at 2.5% per year was $1,000Step-by-step explanation:Letx -----> the amount invested at 4% per year2x ----> the amount invested at 4.5% per year10,000-3x -----> the amount invested at 2.5% per yearwe know thatThe interest earned by the amount invested at 4% per year plus the interest earned by the amount invested at 4.5% per year plus the interest earned by the amount invested at 2.5% per year must be equal to $415so[tex]4\%=4/100=0.04[/tex][tex]4.5\%=4.5/100=0.045[/tex][tex]2.5\%=2.5/100=0.025[/tex][tex]0.04x+0.045(2x)+0.025(10,000-3x)=415[/tex]Solve for x[tex]0.04x+0.09x+250-0.075x=415[/tex][tex]0.055x=415-250[/tex][tex]0.055x=165[/tex][tex]x=\$3,000[/tex]thereforeThe amount invested at 4% per year was $3,000The amount invested at 4.5% per year was $6,000The amount invested at 2.5% per year was $1,000