The cost of apples is increased by 20% and then decreased by 20%. What is the net pecentage decrease?

To find the net percentage decrease, let's break down the problem step by step.

1. **Initial Cost of Apples**: Assume the initial cost of apples is \( C \).

2. **After a 20% Increase**:  
   A 20% increase in cost means the new cost becomes:
   \[
   C_{\text{new}} = C + 0.2C = 1.2C
   \]

3. **After a 20% Decrease**:  
   Now, a 20% decrease is applied to the new cost \( 1.2C \). The cost after this decrease becomes:
   \[
   C_{\text{final}} = 1.2C - 0.2 \times 1.2C = 1.2C \times (1 - 0.2) = 1.2C \times 0.8
   \]
   Simplifying this, we get:
   \[
   C_{\text{final}} = 0.96C
   \]

4. **Net Percentage Decrease**:  
   The net decrease from the original cost \( C \) to the final cost \( 0.96C \) is:
   \[
   \text{Net decrease} = C - 0.96C = 0.04C
   \]
   The percentage decrease is then:
   \[
   \text{Percentage decrease} = \frac{0.04C}{C} \times 100\% = 4\%
   \]

So, the net percentage decrease is **4%**.

Would you like more details or have any questions?

Here are some related questions:
1. What would the net percentage change be if the order of increase and decrease was reversed?
2. How do percentage increases and decreases affect each other multiplicatively?
3. If the cost was increased by 30% and then decreased by 30%, what would be the net percentage change?
4. What happens if the cost is increased and then decreased by different percentages, say 25% and 10% respectively?
5. How can we calculate the overall change if multiple percentage changes are applied sequentially?

**Tip:** When dealing with successive percentage changes, remember that the order of operations matters, and percentage changes are multiplicative, not additive.

Explore how to calculate the net percentage decrease after an initial 20% increase followed by a 20% decrease. Understand the multiplicative effects of percentage changes and learn how to apply them to solve similar problems. Suitable for Grades 6-8 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