Respuesta :
Answer:
• The amount invested at 5.5% = $1400
,• The amount invested at 5% = $1200
Explanation:
The total investment = $2,600
• Let the amount invested at 5.5% = x
,• Let the amount invested at 5% = y
[tex]x+y=2600\cdots(1)[/tex]The total yield on the investments = $137.
[tex]\begin{gathered} \text{ Interest on \$x}=0.055x \\ \text{ Interest on \$y}=0.05y \\ \implies0.055x+0.05y=137\cdots(2) \end{gathered}[/tex]Thus, we have a system of linear equations:
[tex]\begin{gathered} x+y=2600 \\ 0.055x+0.05y=137 \end{gathered}[/tex]From equation (1), x=2600-y. Substitute this into equation (2):
[tex]\begin{gathered} 0.055(2600-y)+0.05y=137 \\ 143-0.055y+0.05y=137 \\ -0.005y=137-143=-6 \\ y=\frac{-6}{-0.005} \\ y=1200 \end{gathered}[/tex]Finally, we find the value of x:
[tex]x=2600-y=2600-1200=1400[/tex]Therefore:
• The amount invested at 5.5% = $1400
,• The amount invested at 5% = $1200
