Question
IF A NUMBER IS INCREASED BY 30% AND DECREASED BY 40% WAT IS THE OVERALL PERCENTAGE CHANGE AND EXPLAIN YOUR ANSWER
Answers
GPT 3.5
To find the overall percentage change, we need to calculate the net effect of increasing the number by 30% and then decreasing it by 40%.
Let's say our original number is "x".
Increasing the number by 30% means adding 30% of x to the original number:
New number = x + 0.3x = 1.3x
Decreasing the number by 40% means subtracting 40% of the new number from it:
New number = 1.3x - 0.4(1.3x) = 1.3x - 0.52x = 0.78x
To calculate the overall percentage change, we compare the difference between the new number and the original number to the original number:
Overall percentage change = (New number - Original number) / Original number * 100
Substituting in the values we found:
Overall percentage change = (0.78x - x) / x * 100 = -0.22x / x * 100 = -22%
Therefore, the overall percentage change is -22%. This means the number decreased by 22% overall.
Let's say our original number is "x".
Increasing the number by 30% means adding 30% of x to the original number:
New number = x + 0.3x = 1.3x
Decreasing the number by 40% means subtracting 40% of the new number from it:
New number = 1.3x - 0.4(1.3x) = 1.3x - 0.52x = 0.78x
To calculate the overall percentage change, we compare the difference between the new number and the original number to the original number:
Overall percentage change = (New number - Original number) / Original number * 100
Substituting in the values we found:
Overall percentage change = (0.78x - x) / x * 100 = -0.22x / x * 100 = -22%
Therefore, the overall percentage change is -22%. This means the number decreased by 22% overall.