Certainly! Let's address the situation with a step-by-step approach to determine whether the businessman can proceed with his donation under the given conditions.
### Step 1: Data Collection and Organization
We'll start by collecting the data for the top ten Mathematics learners, including their gender and shoe sizes.
#### Top 10 Learners Data:
| Learner No. | Gender | Shoe Size |
|-------------|---------|-----------|
| 1 | Male | 8 |
| 2 | Female | 6 |
| 3 | Male | 9 |
| 4 | Female | 7 |
| 5 | Male | 10 |
| 6 | Female | 6 |
| 7 | Male | 8 |
| 8 | Female | 7 |
| 9 | Female | 6 |
| 10 | Female | 5 |
### Step 2: Categorizing Data by Gender
Next, we categorize the data into separate tables for males and females so that we can easily compute their respective donations.
#### Male Learners:
| Learner No. | Shoe Size |
|-------------|-----------|
| 1 | 8 |
| 3 | 9 |
| 5 | 10 |
| 7 | 8 |
#### Female Learners:
| Learner No. | Shoe Size |
|-------------|-----------|
| 2 | 6 |
| 4 | 7 |
| 6 | 6 |
| 8 | 7 |
| 9 | 6 |
| 10 | 5 |
### Step 3: Calculation of Donations for Each Gender
We will calculate the total donation for male and female learners separately. Given the formula for donation is: [tex]\[ \text{Donation} = 50 \times \text{Shoe Size} \][/tex]
#### Male Learners' Donations:
[tex]\[ \text{Donations} = 50 \times (8 + 9 + 10 + 8) \][/tex]
[tex]\[ \text{Donations} = 50 \times 35 \][/tex]
[tex]\[ \text{Donations} = 1750 \text{ currency units} \][/tex]
#### Female Learners' Donations:
[tex]\[ \text{Donations} = 50 \times (6 + 7 + 6 + 7 + 6 + 5) \][/tex]
[tex]\[ \text{Donations} = 50 \times 37 \][/tex]
[tex]\[ \text{Donations} = 1850 \text{ currency units} \][/tex]
### Step 4: Total Donation Calculation
The total donation is the sum of the donations for male and female learners:
[tex]\[ \text{Total Donation} = 1750 + 1850 \][/tex]
[tex]\[ \text{Total Donation} = 3600 \text{ currency units} \][/tex]
### Step 5: Checking Conditions
To conclude if the donation can proceed, we need to check two conditions:
1. The total amount to be donated does not exceed R100,000.
2. The amount of money to be given to girls should be more than the amount given to boys.
From our calculations:
- The total donation (3600) is well below the maximum limit of R100,000.
- The donation to female learners (1850) is greater than the donation to male learners (1750).
### Conclusion
Both conditions for the donation are satisfied:
- The total donation of 3600 currency units does not exceed the maximum limit of R100,000.
- The donation to female learners (1850 currency units) is indeed greater than that to male learners (1750 currency units).
Therefore, the donation is possible according to the given conditions.
