Respuesta :
Answer:
$16,000 at 8% annual interest.
$12,000 at 6% annual interest.
Step-by-step explanation:
Let x be amount invested at a rate of 8% annual interest and y be the amount invested at a rate of 6% annual interest.
We have been given that an executive invests $28000, some at 8% and the rest at 6% annual interest. We can represent this information as:
[tex]x+y=28,000...(1)[/tex]
We are also given that he received annual return of $2000. We can represent this information as:
[tex](\frac{8}{100})x+(\frac{6}{100})y=2,000...(2)[/tex]
[tex]0.08x+0.06y=2,000...(2)[/tex]
We will use substitution method to solve our system of equations. From equation (1) we will get,
[tex]x=28,000-y[/tex]
Substituting this value in equation (2) we will get,
[tex]0.08(28,000-y)+0.06y=2,000[/tex]
[tex]2240-0.08y+0.06y=2,000[/tex]
[tex]2240-2240-0.08y+0.06y=2,000-2240[/tex]
[tex]-0.08y+0.06y=2,000-2240[/tex]
[tex]-0.02y=-240[/tex]
[tex]\frac{-0.02y}{-0.02}=\frac{-240}{-0.02}[/tex]
[tex]y=12,000[/tex]
Therefore, the executive has invested $12,000 at a rate of 6% annual interest.
Upon substituting y=12,000 in equation (1) we will get,
[tex]x+12,000=28,000[/tex]
[tex]x+12,000-12,000=28,000-12,000[/tex]
[tex]x=16,000[/tex]
Therefore, the executive has invested $16,000 at a rate of 8% annual interest.
Answer:
Amount invested at 8% interest rate = $16000
Amount invested at 6% interest rate = $12000
Step-by-step explanation:
Total amount invested = $28000
Let amount invested with 8% interest rate be $x
Then amount invested at 6% interest rate = 28000 - x
Now, Total return = Return from 8% interest rate + Return from 6% interest rate
⇒ 2000 = 8% (in decimal form) × amount invested + 6%(in decimal form) × Amount invested
⇒ 2000 = 0.08 × x + 0.06 × (28000 - x)
⇒ 2000 = 0.02·x + 1680
⇒ x = 16000
Hence, Amount invested at 8% interest rate = $16000
And, Amount invested at 6% interest rate = 28000 - 16000
= $12000
