Roger distributed a total investment of $1000 between mutual funds A

A and B are the amounts invested in each mutual fund.
x and y are the percent of return of each fund.
So we have initially this equations:

\(A + B = 1000\)
\(A*x + B*y = 1.1*(A + B)\)
We have 4 variables and 2 equations


1. "Had he increased the share of mutual fund A in his total investment by 50 percent, he would have received a combined yearly return of 11 percent"

\(A*1.5*x + B*y = 1.11*(A*1.5 + B)\)

With this equation, we have 4 variables and 3 equations, not sufitient.

2. "He received a return of 8 percent from mutual fund B."
This asumption is not a new equation, it just modifies one of the main equations

\(y = 1.08\)
\(A*x + B*(1.08) = 1.1*(A + B)\)
Now we have 3 variables and two equations, not sufitient.

1&2 Combined

\(A + B = 1000\)
\(A*x + B*1.08 = 1.1*(A + B)\)
\(A*1.5*x + B*1.08 = 1.11*(A*1.5 + B)\)
Now we have three equations, and three variables!
But it is not possible to find a solution of this system.

ANS: E


I dont know how to recognize an unsolvable system, it took me a while to find out that there is not possible solution, I dont know a short way to find out.
Also I am not sure if the equations are well "designed", but anyway they still seems to help to get the amount of variables and equations.