Answer
1500 shares of Stock-A, 1200 shares of Stock-B, and 1000 shares of Stock-C,
Work Step by Step
Step 1. Assume the investor owns $x$ shares of Stock-A, $y$ shares of Stock-B, and $z$ shares of Stock-C,
Step 2. As the total value of the investor’s stocks remained unchanged at $74,000$, we can setup the following equations: $10x+25y+29z=12x+20y+32z=16x+15y+32z=74000$
Step 3. As there are two $32z$, we can eliminate that and get $4x=5y$ or $x=\frac{5y}{4}$, use it to back substitute all the $x$ values, we get $\frac{25y}{2}+25y+29z=15y+20y+32z=20y+15y+32z=74000$ which can be simplified to $\frac{75y}{2}+29z=35y+32z=35y+32z=74000$
Step 4. Write the above as two separate equations: $75y+58z=148000$ and $35y+32z=74000$
Step 5. Multiply the first equation by 7 to get $525y+406z=1036000$, multiply the second equation by 15 to get $525y+480z=1110000$
Step 6. Take the difference between the two equations above, we get $74z=74000$ which gives $z=1000$ shares.
Step 7, Back-substitute the know z-value into the earlier equations, we get $y=\frac{74000-32z}{35}=1200$ shares, and $x=\frac{5y}{4}=1500$ shares.
Step 8. We conclude that the investor owns 1500 shares of Stock-A, 1200 shares of Stock-B, and 1000 shares of Stock-C,
