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, let's break down the problem step by step.
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Initial Cost of Apples: Assume the initial cost of apples is .
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After a 20% Increase:
A 20% increase in cost means the new cost becomes: -
After a 20% Decrease:
Now, a 20% decrease is applied to the new cost . The cost after this decrease becomes: Simplifying this, we get: -
Net Percentage Decrease:
The net decrease from the original cost to the final cost is: The percentage decrease is then:
So, the net percentage decrease is 4%.
Would you like more details or have any questions?
Here are some related questions:
- What would the net percentage change be if the order of increase and decrease was reversed?
- How do percentage increases and decreases affect each other multiplicatively?
- If the cost was increased by 30% and then decreased by 30%, what would be the net percentage change?
- What happens if the cost is increased and then decreased by different percentages, say 25% and 10% respectively?
- 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.
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Math Problem Analysis
Mathematical Concepts
Percentage Change
Multiplicative Effects of Percentages
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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