Phase 1: Owning the Dataset
Visual Representation
Let's create a simple table to organize our information:
| Employee |
Base Salary (KES) |
Bonus % |
Bonus Amount (KES) |
| Winnie |
4,600,000 |
\(\mathrm{p\%}\) |
? |
| Ali |
3,400,000 |
\(\mathrm{p\%}\) |
? |
| Total |
8,000,000 |
|
560,000 |
Key insight: Both employees receive the same percentage \(\mathrm{(p\%)}\) of their base salaries as bonuses.
Phase 2: Understanding the Question
We need to find:
- Winnie's bonus amount
- Ali's bonus amount
Since they both get the same percentage of their salaries, and the total bonus is 560,000 KES, we can set up an equation:
Winnie's bonus + Ali's bonus = 560,000
\(\mathrm{(4,600,000 \times p\%) + (3,400,000 \times p\%) = 560,000}\)
Phase 3: Finding the Answer
Step 1: Find the percentage
Let's factor out \(\mathrm{p\%}\):
\(\mathrm{p\% \times (4,600,000 + 3,400,000) = 560,000}\)
\(\mathrm{p\% \times 8,000,000 = 560,000}\)
Therefore:
\(\mathrm{p\% = 560,000 ÷ 8,000,000}\)
\(\mathrm{p\% = 0.07 = 7\%}\)
Step 2: Calculate individual bonuses
Winnie's bonus:
\(\mathrm{4,600,000 \times 7\% = 4,600,000 \times 0.07 = 322,000\text{ KES}}\)
Ali's bonus:
\(\mathrm{3,400,000 \times 7\% = 3,400,000 \times 0.07 = 238,000\text{ KES}}\)
Verification
Let's confirm: \(\mathrm{322,000 + 238,000 = 560,000}\) (checkmark)
Phase 4: Solution
Looking at our answer choices: [216,000, 238,000, 256,000, 304,000, 322,000]
Final Answer:
- Winnie: 322,000 KES
- Ali: 238,000 KES
