Suppose an amount increases by 100%, then decreases by 100%. Find the final amount. Would the situation change if the original increase was 150%? Explain your reasoning.
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anything that decreases by 100% ends up at zero.
To find the final amount in these scenarios, we need to understand the concept of percent increase and decrease.
Let's start with the first scenario:
1. Suppose an amount increases by 100%.
This means the original value has doubled. If the original value is x, after the 100% increase, the new value will be 2x.
2. Then, the amount decreases by 100%.
A decrease of 100% means the value is reduced to zero. So, the new value is 0.
Therefore, the final amount is 0.
Now let's consider the second scenario where the original increase is 150%:
1. Suppose an amount increases by 150%.
This means the original value is multiplied by 1.5. If the original value is x, after the 150% increase, the new value will be 1.5x.
2. Then, the amount decreases by 100%.
Similar to the previous scenario, a decrease of 100% means the value is reduced to zero. So, the new value is 0.
Therefore, in both scenarios, the final amount is 0. The size of the original increase does not affect the final outcome in this particular case.
To find the final amount, we first need to understand what it means when an amount increases or decreases by a certain percentage.
Let's assume the original amount is 100 units.
If an amount increases by 100%, it means it doubles in size. So, increasing the original amount of 100 units by 100% gives us an additional 100 units for a total of 200 units.
Now, if the amount decreases by 100%, it means it goes back to its original value or becomes zero. So, decreasing the 200 units by 100% gives us zero.
Therefore, the final amount is 0.
Now, let's consider the case where the original increase is 150%.
Assuming the original amount is 100 units again, increasing it by 150% means increasing it by 1.5 times. So, the increase would be 100 units x 1.5 = 150 units.
If the amount decreases by 100%, it goes back to its original value. So, the final amount would be 100 units.
In conclusion, if the original increase was 150%, the final amount would be 100 units.