If his overall profit for the year was $\$104.50$, and he invested $300 more in commodities than in REITs, how much was allocated to each investment?

Question

Through monthly deductions from his salary, Noah managed to accumulate 4800 per month last year for his future sabbatical trip. His savings account yielded 4.2% interest, his real estate investment trust (REIT) gained 5.75%, but his commodity portfolio dipped by 2.5%. If his overall profit for the year was $104.50, and he invested 300 more in commodities than in REITs, how much was allocated to each investment category? (Formulate a system of equations and solve it by utilizing the inverse matrix method.)

I am sure about two equations:
His overall profit for the year is 104.50: $0.042S + 0.0575R - 0.025C = 104.50$
The amount invested in commodities is 300 more than the amount invested in REITs: $C = R + 300$
But im not too sure how to get the 3rd equation. I have two candidates:

The total amount invested is 4800 per month: $S + R + C = 4800$
or
The total amount invested is 4800 per month, so in a year it would be 57600 : $S + R + C = 57600.$

Im not sure which one to use and why would i use it.

Answer 1

This is more of an English question than math, but it should be the second equation because the question states "accumulate 4800 per month", while the interest rates are typically per year. However, this results in a negative amount contributed to savings...

This also depends on whether "he invested 300 more in commodities than in REITs" per month or per year, which would change the second equation.

The answer also changes depending on how the interest is accrued -- the first equation might not just be 4.2% of S + the rest = 104.50 because the contributions are monthly so less interest is accrued when there is less money in the account. Assuming no compounding in the savings account, contributing $S/12$ every month, in the first month it would be 4.2%/12 of $S/12$, then 4.2%/12 of $2S/12$ the next month, etc.