Que - 31
Directions (31-35): Study the following passage carefully and answer the questions given
below.
The data given below is about number of shoes and bags sold by four different stores. Total
number of bags sold by all four stores is 514 which is 50 more than sum of total number of
items sold by N and P. Number of shoes sold by P is 4 more than half of number of shoes sold
by M. Number of bags sold by O is 150. The ratio of number of bags to number of shoes sold by
O is (p+2):(1.5q+p). Number of bags sold by N is 33.33% less than number of shoes sold by N
and number of bags sold by P is 2(p+q) less than number of bags sold by O.Total number of
items sold by O is 330 which 42 more than total number of items sold by M. Number of shoes
sold by N is 12.5% more than number of bags sold by M

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?

Que - 31 Directions (31-35): Study the following passage carefully and answer the questions given below. The data given below is about number of shoes and bags sold by four different stores. Total number of bags sold by all four stores is 514 which is 50 more than sum of total number of items sold by N and P. Number of shoes sold by P is 4 more than half of number of shoes sold by M. Number of bags sold by O is 150. The ratio of number of bags to number of shoes sold by O is (p+2):(1.5q+p). Number of bags sold by N is 33.33% less than number of shoes sold by N and number of bags sold by P is 2(p+q) less than number of bags sold by O. Total number of items sold by O is 330 which 42 more than total number of items sold by M. Number of shoes sold by N is 12.5% more than number of bags sold by M.

This problem explores algebraic relationships between shoes and bags sold by four stores. Solve using concepts of percentages, ratios, and linear equations. Suitable for students in Grades 9-11.

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