Respuesta :
Answer:
$2500 at 8%.
$2900 st 5%.
Step-by-step explanation:
Let x be the amount invested at rate of 8% and y be the amount invested at the rate of 5%.
We have been given that Heather has divided $5400 between two investments. We can represent this information as:
[tex]x+y=5400...(1)[/tex]
The return on her investment is $345.
Earnings from the investment at 8% will be 8% of x.
Earnings from the investment at 5% will be 5% of y.
[tex](\frac{8}{100})x+(\frac{5}{100})y=345...(2)[/tex]
[tex]0.08x+0.05y=345...(2)[/tex]
We will use substitution method to solve our system of equations. From equation (1) we will get,
[tex]x=5400-y[/tex]
Substituting this value in equation (2) we will get,
[tex]0.08(5400-y)+0.05y=345[/tex]
[tex]432-0.08y+0.05y=345[/tex]
[tex]-0.08y+0.05y=345-432[/tex]
[tex]-0.03y=-87[/tex]
[tex]\frac{-0.03y}{-0.03}=\frac{-87}{-0.03}[/tex]
[tex]y=2900[/tex]
Therefore, Heather has invested an amount of $2900 at 5%.
Let us substitute y=2900 in equation (1) to solve for x.
[tex]x+2900=5400[/tex]
[tex]x+2900-2900=5400-2900[/tex]
[tex]x=2500[/tex]
Therefore, Heather has invested an amount of $2500 at 8%.
