Anna asks her broker to divide her investment of $2000 among three funds, X, Y, and Z. She decides that her investment in X should be twice her investment in Z. During the first quarter, X earned 4.5%, Y earned 2.6%, and Z lost 0.2%. Anna earned $58 on her investment during that period. How many dollars did the broker put into each fund?

Question

anonymous · Answer

$$
x+y+z = 2000
$$$$
0.045x+0.026y-0.002z = 58
$$

anonymous · Answer

$$
x  = 2z
$$

anonymous · Answer

This is a matrix: $$
\begin{bmatrix}
1&1&1\
0.045&0.026&0.002 \
1&0&-2 
\end{bmatrix}
\begin{bmatrix}
x\y\z
\end{bmatrix}
=
\begin{bmatrix}
2000\58\0
\end{bmatrix}
$$