Answer :
SOLUTION
We want to find the principal money borrowed each at 13% and 15% from a total money of $25,000.
Now, let the money he borrowed at 15% be x
and, let the money he borrowed at 13% be y.
This means that
[tex]\begin{gathered} x+y=25,000 \\ \text{and } \\ y=25,000-x \end{gathered}[/tex]From the simple interest formula
[tex]\begin{gathered} I=\frac{PRT}{100} \\ \text{Where, I = interest, P = principal, R = rate and T = time } \end{gathered}[/tex]Interest on 15% will be
[tex]\begin{gathered} I_{15}=\frac{x\times15\times1}{100} \\ I_{15}=0.15x \end{gathered}[/tex]Interest on 13% will be
[tex]\begin{gathered} I_{13}=\frac{(25000-x)\times13\times1}{100} \\ I_{13}=(25000-x)\times0.13 \\ I_{13}=3250-0.13x \end{gathered}[/tex]Now, both interest should be = $3,600
That is
[tex]\begin{gathered} I_{15}+I_{13}=3,600 \\ 0.15x+(3250-0.13x)=3,600 \\ 0.15x-0.13x=3,600-3250 \\ 0.02x=350 \\ x=\frac{350}{0.02} \\ x=17,500 \end{gathered}[/tex]So, the money he borrowed at 15% is $17,500
And the money he borrowed at 13% is
[tex]25000-17500=7,500[/tex]Hence, the answer is $17,500 at 15% and $7,500 at 13%.