Respuesta :
Answer:
$7,000 at a rate of 7% and $21,000 at a rate of 14%.
Step-by-step explanation:
Let x be amount invested at 7% and y be amount invested at 14%.
We have been given that a women's professional organization made two small-business loans totaling $28,000. We can represent this information in an equation as:
[tex]x+y=28,000...(1)[/tex]
The interest earned at 7% in one year would be [tex]0.07x[/tex] and interest earned at 14% in one year would be [tex]0.14x[/tex].
We are also told that the organization received from these loans was $3,430. We can represent this information in an equation as:
[tex]0.07x+0.14y=3,430...(2)[/tex]
Form equation (1), we will get:
[tex]x=28,000-y[/tex]
Upon substituting this value in equation (2), we will get:
[tex]0.07(28,000-y)+0.14y=3,430[/tex]
[tex]1960-0.07y+0.14y=3,430[/tex]
[tex]1960+0.07y=3,430[/tex]
[tex]1960-1960+0.07y=3,430-1960[/tex]
[tex]0.07y=1470[/tex]
[tex]\frac{0.07y}{0.07}=\frac{1470}{0.07}[/tex]
[tex]y=21,000[/tex]
Therefore, an amount of $21,000 was invested at a rate of 14%.
[tex]x=28,000-y[/tex]
[tex]x=28,000-21,000[/tex]
[tex]x=7,000[/tex]
Therefore, an amount of $7,000 was invested at a rate of 14%.
