Respuesta :
Answer:
Amount invested at a rate of 6% = [tex]\$400[/tex]
Amount invested at a rate of 7% = [tex]\$1600[/tex]
Explanation:
Let x and y denote the amount of money, in dollars, invested at 6% and 7%, respectively.
Total amount deposited = $2000
[tex]x+y=2000[/tex]
[tex]x=2000-y[/tex]
Interest earned on amount [tex]x[/tex] = [tex]\frac{6}{100}x[/tex]
Interest earned on amount [tex]y[/tex] = [tex]\frac{7}{100}y[/tex]
Total interest earned [tex]=\frac{6}{100}x+\frac{7}{100} y[/tex]
As Michael earned a total of $136 in interest during a single year,
[tex]\frac{6}{100}x+\frac{7}{100} y=136\\6x+7y=13600[/tex]
Put [tex]x=2000-y[/tex]
[tex]6(2000-y)+7y=13600\\12000-6y+7y=13600\\12000+y=13600\\y=13600-12000\\y=1600[/tex]
So,
[tex]x=2000-1600=400[/tex]
Amount invested at a rate of 6% = [tex]\$400[/tex]
Amount invested at a rate of 7% = [tex]\$1600[/tex]
