LET General Education Mathematics: Two-Rate Commission Problems
Commission problems involving different percentage rates are common examples of multi-step percentage computations. To solve them correctly, examine the commission brackets carefully because each portion of the sales may have a different commission rate.
Let's study this LET General Education Mathematics practice question and learn how to calculate commission when two different rates are applied.
LET Practice Question
Question: A salesman gets 12% commission for the first ₱15,000 and 10% for the amount over ₱15,000 of his total sales. How much does he get for a total sales of ₱30,600?
- ₱3,400
- ₱3,360
- ₱3,340
- ₱3,460
Correct Answer: B. ₱3,360
Step-by-Step Solution
The problem provides two commission rates:
- 12% for the first ₱15,000 in sales.
- 10% for the amount exceeding ₱15,000.
The total sales are ₱30,600. We must calculate the commission for each portion separately and then add the results.
Step 1: Calculate the Commission on the First ₱15,000
Formula:
Commission = Sales Amount × Commission Rate
Substitute the given values:
₱15,000 × 0.12 = ₱1,800
Therefore, the commission for the first ₱15,000 is ₱1,800.
Step 2: Calculate the Excess Sales
The total sales are ₱30,600, but the first ₱15,000 already has its own commission rate.
Excess Sales = Total Sales − First Sales Bracket
₱30,600 − ₱15,000 = ₱15,600
Therefore, the excess sales amount is ₱15,600.
Step 3: Calculate the Commission on the Excess
The excess sales earn a 10% commission.
₱15,600 × 0.10 = ₱1,560
Therefore, the commission on the excess sales is ₱1,560.
Step 4: Add the Two Commission Amounts
Total Commission = First Commission + Second Commission
₱1,800 + ₱1,560 = ₱3,360
Therefore, the correct answer is Letter B. ₱3,360.
LET Board Exam Tip: Different Commission Brackets
When a Mathematics problem gives different commission rates for different sales amounts, remember these steps:
- Identify the first sales bracket and its corresponding commission rate.
- Calculate the excess sales by subtracting the first bracket from total sales.
- Apply the appropriate commission rate to the excess amount.
- Add all commission amounts to get the total commission.
Important reminder: Do not apply the first commission rate to the entire sales amount. Each sales portion must use its corresponding rate.
Key Takeaway
For tiered commission problems, calculate each bracket separately before adding the results. Understanding the structure of the problem helps prevent common mistakes in percentage computations.
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This article is intended for educational review and LET/LEPT preparation. It is not an official PRC publication.