Math Problem Statement
The cost of apples is increased by 20% and then decreased by 20%. What is the net pecentage decrease?
Solution
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 .
After a 20% increase:
Step 2: Subsequent Decrease by 20%
Now, decrease the increased price by 20%:
Step 3: Calculate the Net Change
The final cost of the apples is , which is 96% of the original cost .
So, the net percentage decrease is:
Answer:
The net percentage decrease is 4%.
Would you like more details, or do you have any questions?
Here are five related questions:
- What would be the net percentage change if the cost is first decreased by 20% and then increased by 20%?
- How would the net percentage change if the increase and decrease percentages were different (e.g., 25% increase and 20% decrease)?
- What happens to the net percentage change if the increase and decrease are the same percentage but reversed in order?
- 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)?
- Can you generalize the formula for net percentage change when increasing by and then decreasing by ?
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.
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Math Problem Analysis
Mathematical Concepts
Percentage Change
Sequential Percentage Change
Formulas
Percentage Increase Formula
Percentage Decrease Formula
Theorems
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Suitable Grade Level
Grades 7-9
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