Let's break down the information from the passage step by step.

Key Variables:

Let:

• $M_s$ = Number of shoes sold by M
• $N_s$ = Number of shoes sold by N
• $O_s$ = Number of shoes sold by O
• $P_s$ = Number of shoes sold by P
• $M_b$ = Number of bags sold by M
• $N_b$ = Number of bags sold by N
• $O_b$ = Number of bags sold by O
• $P_b$ = Number of bags sold by P

Key Information:

1. Total Bags Sold: $M_b + N_b + O_b + P_b = 514$ Total number of bags sold by all four stores is 514, and this is 50 more than the total number of items sold by N and P. This implies: $(N_s + N_b) + (P_s + P_b) = 514 - 50 = 464$

2. Shoes Sold by P: The number of shoes sold by P is 4 more than half the number of shoes sold by M: $P_s = \frac{M_s}{2} + 4$

3. Bags Sold by O: The number of bags sold by O is given as: $O_b = 150$

4. Ratio for O: The ratio of the number of bags to the number of shoes sold by O is $(p+2):(1.5q+p)$, where the exact values of $p$ and $q$ are not given. We’ll hold this information for now.

5. Bags Sold by N: The number of bags sold by N is 33.33% less than the number of shoes sold by N: $N_b = N_s - \frac{33.33}{100} \times N_s = \frac{2}{3} N_s$

6. Bags Sold by P: The number of bags sold by P is $2(p+q)$ less than the number of bags sold by O: $P_b = O_b - 2(p+q) = 150 - 2(p+q)$

7. Total Items Sold by O: The total number of items sold by O is 330, which is 42 more than the total number of items sold by M: $O_s + O_b = 330$ $M_s + M_b = 330 - 42 = 288$

8. Shoes Sold by N: The number of shoes sold by N is 12.5% more than the number of bags sold by M: $N_s = M_b + \frac{12.5}{100} \times M_b = 1.125 \times M_b$

Step-by-Step Approach:

We have multiple variables and equations. Let's solve them systematically.

• Start by solving for $O_s$ using $O_s + O_b = 330$: $O_s + 150 = 330 \quad \Rightarrow \quad O_s = 180$

• Next, use the total number of items sold by M to set up an equation for $M_s + M_b = 288$.

We can continue solving this system of equations to find the exact values of $M_s$, $N_s$, $P_s$, etc., by substituting one into the other.

Would you like me to proceed with the detailed calculations?