https://file.aiquickdraw.com/mathbot/file/1730807256074n4oyfchg.jpg

To solve the problem, let's analyze the information provided in the table and follow through with the steps necessary to find the answer.

### Step 1: Extract Information
The table provides:
1. The total number of workers in each factory (P, Q, R, S, T).
2. The number of workers aged over 45 in each factory.
3. The ratio of male to female workers over 45 in each factory.

Factories and their dataTo solve the problem, let's analyze the information provided in the table and follow through with the steps necessary to find the answer.

### Step 1: Extract Information
The table provides:
1. The total number of workers in each factory (P, Q, R, S, T).
2. The number of workers aged over 45 in each factory.
3. The ratio of male to female workers over 45 in each factory.

Factories and their 
- **P**: Total = 120, Over 45 = 70, Male:Female = 1:4
- **Q**: Total = 60, Over 45 = 30, Male:Female = 1:1
- **R**: Total = 90, Over 45 = 40, Male:Female = 3:2
- **S**: Total = 80, Over 45 = 50, Male:Female = 2:3
- **T**: Total = 110, Over 45 = 30, Male:Female = 1:1

### Step 2: Calculate Male and Female Workers Over 45 in Each Factory
Using the male-to-female ratios, we can split the "over 45" workers into male and female categories.

#### Factory P
- Ratio: 1:4 → Male = 1/5, Female = 4/5
- Males = \( 70 \times \frac{1}{5} = 14 \)
- Females = \( 70 \times \frac{4}{5} = 56 \)

#### Factory Q
- Ratio: 1:1 → Male = 1/2, Female = 1/2
- Males = \( 30 \times \frac{1}{2} = 15 \)
- Females = \( 30 \times \frac{1}{2} = 15 \)

#### Factory R
- Ratio: 3:2 → Male = 3/5, Female = 2/5
- Males = \( 40 \times \frac{3}{5} = 24 \)
- Females = \( 40 \times \frac{2}{5} = 16 \)

#### Factory S
- Ratio: 2:3 → Male = 2/5, Female = 3/5
- Males = \( 50 \times \frac{2}{5} = 20 \)
- Females = \( 50 \times \frac{3}{5} = 30 \)

#### Factory T
- Ratio: 1:1 → Male = 1/2, Female = 1/2
- Males = \( 30 \times \frac{1}{2} = 15 \)
- Females = \( 30 \times \frac{1}{2} = 15 \)

### Step 3: Calculate the Difference Between Female and Male Workers Over 45
Now, we calculate the difference between the total female and male workers over 45 across all factories.

\[
\text{Total Males} = 14 + 15 + 24 + 20 + 15 = 88
\]
\[
\text{Total Females} = 56 + 15 + 16 + 30 + 15 = 132
\]
\[
\text{Difference (Females - Males)} = 132 - 88 = 44
\]

### Conclusion
The difference between the number of female and male workers over 45 is **44**. 

**Answer: C (44)**

Would you like a further breakdown of any part of this solution? 

Here are some related questions to explore:
1. What if the ratio of male-to-female workers was different in one of the factories? How would it affect the outcome?
2. How would the answer change if the total number of workers over 45 in factory S was different?
3. If the percentage of male workers over 45 changes, how can we adjust our calculations?
4. Can this method be applied to any other similar workforce distribution problems?
5. How can we verify the accuracy of ratios in real-world scenarios?

**Tip:** Understanding ratios allows for flexible calculations in various scenarios, helping break down complex distributions like workforce demographics.

A set of factories have employees over the age of 45. The table shows each factory's total employees, number of employees over 45, and the male-to-female ratio for employees over 45. Calculate the difference between the number of female and male workers over 45.

Learn to calculate the difference between the number of female and male workers over the age of 45 across multiple factories, using ratios and percentages. This example involves understanding workforce demographics and applying ratio-based calculations. Suitable for Grade 11-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation