IF A NUMBER IS INCREASED BY 30% AND DECREASED BY 40% WAT IS THE OVERALL PERCENTAGE CHANGE AND EXPLAIN YOUR ANSWER
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.
To find the overall percentage change, we need to calculate the individual percentage changes first.
Let's assume the initial number is x.
When the number is increased by 30%, the increase is given by 0.3x.
So, the new number is x + 0.3x = 1.3x.
Now, when the number is decreased by 40%, the decrease is given by 0.4(1.3x).
So, the final number is 1.3x - 0.4(1.3x) = 1.3x - 0.52x = 0.78x.
To find the overall percentage change, we need to find the difference between the final number and the initial number, and then divide it by the initial number. Finally, we multiply by 100 to express it as a percentage.
Overall percentage change = [(0.78x - x)/x] * 100
Simplifying the expression inside the brackets:
Overall percentage change = [-0.22x/x] * 100
Overall percentage change = -22%
Therefore, the overall percentage change is -22%. This implies there has been a decrease of 22% in the initial number after the given operations.