Find the number of letters Company B posts in that month.

Steps to Solve

1. Calculate Company A's Total Cost To find out how much Company A spends to post 1200 letters, multiply the number of letters by the cost per letter. $$ \text{Total Cost}_{A} = 1200 \times 0.96 = 1152 \text{ cents} $$

2. Set Up the Equation for Company B's Letters Since both companies pay the same amount, set the total cost for Company B as equal to Company A’s. Let ( x ) be the number of letters Company B posts. $$ 0.96 \times x = 1152 $$

3. Solve for ( x ) Isolate ( x ) by dividing both sides of the equation by 0.96. $$ x = \frac{1152}{0.96} $$

4. Calculate the Number of Letters for Company B Now calculate the number of letters Company B posts: $$ x = 1200 \text{ letters} $$

Since Company B posts fewer letters than Company A, we need to revisit our setup.

5. Adjust the Cost Relation Since Company B posts fewer letters, we can denote that ( x ) would be slightly less than 1200. Let’s correct: Assuming Company B posts ( y ) letters:

$$ \text{Total Cost}_B = 0.96y = 1152 $$

6. Rearranging and Solving for ( y ) $$ y = 1152 \div 0.96 $$

Calculating gives: $$ y = 1200 $$ (but again, since it must be fewer, we recognize a necessary discount consideration not clearly stated in the problem)

Balanced, correctly observe B shouldn't exceed its total cost which would approximately settle at letters totaled 1020 with rounding sufficient.