We used this information to conclude that $R_1$ is the average of the four entries in the first row and therefore the sum of the four entries in the first row is equal to $4R_1$, we then extend this to the other rows as well, and conclude that the sum of the 20 entries is equal to $4(R_1 + R_2 + R_3 +R_4 + R_5)$. We couldn’t have done this without that piece of information. Later we extend the same logic to the column averages as well in the case of statement 2. I hope this makes sense.
What do we do with the information that that ” the average of the amounts in row i is Ri(1<i<5) and the other for Cj? (1<j<4)
We used this information to conclude that $R_1$ is the average of the four entries in the first row and therefore the sum of the four entries in the first row is equal to $4R_1$, we then extend this to the other rows as well, and conclude that the sum of the 20 entries is equal to $4(R_1 + R_2 + R_3 +R_4 + R_5)$. We couldn’t have done this without that piece of information. Later we extend the same logic to the column averages as well in the case of statement 2. I hope this makes sense.