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 after the cost of apples is first increased by 20% and then decreased by 20%, let's work through the problem step by step.

### Step 1: Initial Increase by 20%
Let the original cost of the apples be $ C $.

After a 20% increase:
\[
\text{New Cost} = C \times (1 + 0.20) = 1.2C
\]

### Step 2: Subsequent Decrease by 20%
Now, decrease the increased price by 20%:
\[
\text{Final Cost} = 1.2C \times (1 - 0.20) = 1.2C \times 0.80 = 0.96C
\]

### Step 3: Calculate the Net Change
The final cost of the apples is $ 0.96C $, which is 96% of the original cost $ C $.

So, the net percentage decrease is:
\[
\text{Net Percentage Decrease} = \left(1 - 0.96\right) \times 100\% = 0.04 \times 100\% = 4\%
\]

### Answer:
The net percentage decrease is **4%**.

Would you like more details, or do you have any questions?

Here are five related questions:
1. What would be the net percentage change if the cost is first decreased by 20% and then increased by 20%?
2. How would the net percentage change if the increase and decrease percentages were different (e.g., 25% increase and 20% decrease)?
3. What happens to the net percentage change if the increase and decrease are the same percentage but reversed in order?
4. How would the net percentage change if both increase and decrease percentages are the same, but in absolute terms (e.g., increase by $2 and decrease by $2)?
5. Can you generalize the formula for net percentage change when increasing by $ x\% $ and then decreasing by $ y\% $?

**Tip:** When percentages are applied sequentially, the order and the magnitude of changes affect the final result. Always be careful not to assume that the effects cancel each other out perfectly.

Learn how to calculate the net percentage decrease after increasing the cost of apples by 20% and then decreasing it by 20%. Follow a detailed step-by-step solution covering percentage increase and decrease formulas. Suitable for students in Grades 7-9.

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