LET GENERAL EDUCATION REVIEWER
RATIO AND PROPORTION
Practice Question | Correct Answer | Detailed Rationale
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Introduction
Mathematics is an important component of the General Education portion of the Licensure Examination for Professional Teachers (LET/LEPT). Examinees should understand basic mathematical concepts and develop the ability to solve practical word problems.
One frequently encountered mathematical concept is ratio and proportion. This concept helps us compare quantities and solve problems involving prices, distances, time, measurements, and other real-life situations.
In this LET practice question, we will learn how to solve a problem involving the price of apples using the unitary method and direct proportion.
Table of Contents
LET Practice Question
Question:
Felnie buys 3 apples for P50. How much does she pay for a dozen of these apples?
A. P150
B. P220
C. P200
D. P180
Correct Answer
C. P200
The cost of 12 apples is P200.
Detailed Rationale
To solve this problem, we need to understand the relationship between the number of apples and their total cost.
Given:
- 3 apples cost P50.
- One dozen is equivalent to 12 pieces.
- We need to find the cost of 12 apples.
Method 1: Using Direct Proportion
Since 12 apples are four times the quantity of 3 apples, multiply the original price by 4.
12 ÷ 3 = 4
P50 × 4 = P200
Final Answer: P200
Method 2: Using the Unitary Method
The unitary method involves finding the value of one unit before calculating the value of the required quantity.
Step 1: Find the price of one apple.
P50 ÷ 3 = P16.6667 approximately.
Step 2: Multiply by 12 apples.
P16.6667 × 12 = P200.
Therefore, 12 apples cost P200.
Analysis of All Choices
Option A: P150 – Incorrect
P150 is equivalent to the cost of 9 apples because 3 groups of 3 apples cost 3 × P50 = P150. It does not represent the price of 12 apples.
Option B: P220 – Incorrect
P220 does not follow the proportional relationship established in the problem. Four groups of 3 apples would cost P200, not P220.
Option C: P200 – Correct
One dozen is 12 apples. Since 12 is four times 3, multiply P50 by 4. The correct amount is P200.
Option D: P180 – Incorrect
P180 does not represent the correct cost of 12 apples based on the given price. The proportional computation produces P200.
Key Mathematical Concepts to Remember
1. Ratio
A ratio is a comparison of two quantities using division. For example, the ratio of 3 apples to 12 apples is 3:12, which simplifies to 1:4.
2. Proportion
A proportion is an equality between two ratios. It is useful when determining an unknown quantity based on a known relationship.
3. Direct Proportion
Two quantities are directly proportional when an increase in one quantity results in a corresponding increase in the other, assuming their constant rate of relationship remains unchanged.
In this problem, the number of apples and the total price are directly proportional because the price per apple remains constant.
4. Unitary Method
The unitary method is a mathematical technique in which we first determine the value of one unit and then multiply it by the required number of units.
Real-Life Application
Understanding direct proportion is useful in everyday situations, particularly when purchasing goods.
For example, if 5 notebooks cost P100, how much will 15 notebooks cost at the same unit price?
Since 15 is three times 5:
P100 × 3 = P300.
This demonstrates how the unitary method and direct proportion can help students calculate prices accurately.
LET Examination Tips
- Read the question carefully. Identify the given quantity and the quantity being asked.
- Remember basic conversions. One dozen is equal to 12 pieces.
- Identify the relationship. Determine whether the problem involves direct or inverse proportion.
- Use shortcuts when possible. If the required quantity is a simple multiple of the given quantity, multiply the corresponding price by the same factor.
- Check your answer. Make sure the final amount is reasonable based on the given information.
Memory Aid
UNITARY METHOD:
Find ONE unit first, then MULTIPLY by the required quantity.
DIRECT PROPORTION:
More quantity = More total cost, when the unit price remains constant.
Remember: Same rate, same relationship!
Frequently Asked Questions
1. How many apples are in one dozen?
One dozen is equivalent to 12 pieces, regardless of the type of item being counted.
2. What is the unitary method in Mathematics?
The unitary method is a process of finding the value of one unit first and using that value to calculate the cost or quantity of multiple units.
3. How can I quickly solve direct proportion problems in the LET?
Compare the required quantity with the given quantity. If the required quantity is a simple multiple of the given quantity, multiply the corresponding value by the same factor.
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Final Encouragement for Future LPTs
Every practice question is an opportunity to improve your understanding and develop your confidence. Do not be discouraged by challenging Mathematics problems. Learn the concepts, practice consistently, and understand the rationale behind every answer.
Keep preparing for your dream of becoming a licensed professional teacher!
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