Answer
$2500$ dollars in Bank A, $40000$ dollars in Bank B, $17500$ dollars in Bank C.
Work Step by Step
Step 1. Assume she invested $x$ amount in Bank A, $y$ amount in Bank B, and $z$ amount in Bank C.
Step 2. Based on the conditions given, we can set up the following system of equations:
$\begin{cases} x+y+z=60000\hspace3cm(total-amount) \\y=2(x+z)\\0.02x+0.025y+0.03z=1575\hspace1cm(total-interests) \end{cases}$
Step 3. Multiply 1000 to remove the decimals in the third equation and use the second equation for substitutions:
$\begin{cases} x+2(x+z)+z=60000 \\y=2(x+z)\\20x+25\times2(x+z)+30z=1575000 \end{cases}$
Step 4. Cancel common factors in the third equation and combine like terms:
$\begin{cases} x+z=20000 \\y=2(x+z)\\14x+16z=315000 \end{cases}$
Step 5. Combine the first two equations gives $y=40000$. The first equation gives $z=20000-x$, use it in the third equation to give $14x+16(20000-x)=315000$ or $x=2500$, thus $z=17500$
Step 6. Conclusion: she invested $2500$ dollars in Bank A, $40000$ dollars in Bank B, and $17500$ dollars in Bank C.
