# Percents: Percent Change

The gross national product (GNP) of Andalasia decreased by 25% due to a financial crisis. Then due to a trade war with Actasia, the GNP decreased by an additional 10%. By approximately what percent would the GNP now have to increase by in order to restore it to its original amount?
Incorrect. [[snippet]] 32.5% is the total amount that the GNP decreased, but the percent decrease and the percent increase needed to undo that are not equal. Imagine decreasing by 99% and then increasing the result by 99%. This is a common mistake that can be avoided by **Plugging In** a value for the initial value.
Incorrect. [[snippet]] A common mistake is to add the percent changes in the problem, without considering the original amount. In this question, the GNP decreased by 25% and then by an additional 10%. Since the 10% decrease is not on the original amount, the total percent decrease is not 35%. Additionally, the percent decrease is not equal to the required percent increase to end up back at the starting point. Consider decreasing by 50% and then increasing by 50%.
Correct. [[snippet]] Start by **Plugging In** 100 for the initial GNP. Then, deduct 25% to get 75. Finally, deduct 10% of that (7.5) to get $$\text{GNP}_\text{final} = 67.5$$. In order to restore the GNP to its original amount, Andalasia needs to add 32.5 to the current GNP. Set up the percent change formula to help you **Ballpark** the answer. >$$\displaystyle \mbox{Percent Change}=\frac{\mbox{Difference}}{\mbox{Original}}\cdot100\%$$ >$$\displaystyle \mbox{Percent Change}=\frac{32.5}{67.5}\cdot100\%$$ Such messy numbers can make you weep! But notice that 32.5 is a bit less than 67.5. That means that the answer is a bit less than 50%. 48% is the only answer in that ballpark, so it must be the correct answer.
Incorrect. [[snippet]] You may have gotten this answer if you thought that the GNP decreased by 35% in total. Remember that the decrease of 10% happened after the decrease of 25%, so it isn't a decrease on the original amount. **Plug In** for the initial amount and do the math.
Incorrect. [[snippet]] 67.5% is the percent remaining after the decreases. The question, though, asks you for the percent increase needed to return the GNP to the original amount.
32.5%
35%
48%
56%
67.5%

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