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# Percents: Percent Change

Aaron's accountant accidentally decreased the salary of an employee by 25% instead of giving her a 25% increase. After receiving her paycheck, the employee complained to Aaron. The accountant was asked to fix the mistake by giving the employee a check for the missing amount. The make-up check is approximately what percent of the erroneous paycheck?
Incorrect. [[snippet]] __Plug In__ 100 for the employee's salary (the invisible variable) to demonstrate that if you decrease it by 25% ($$100-25=75$$), then an 80% check on 75 will be 60 ($$75\cdot 0.8 = 60$$). The employee's paycheck should have been $$100+25 = 125$$. A check of 60 would be too much.
Correct. [[snippet]] __Plug In__ 100 for the employee's original salary (the invisible variable). After the accidental decrease of 25%, the employee's salary becomes $$100-25=75$$. The intended increase in the employee's salary should have resulted in $$100+25=125$$. To fix that, the accountant needs to give the employee a check for 50. Use the percent change formula: >$$\displaystyle \text{Percent change}=\frac{\text{Difference}}{\text{Original}} \times 100$$. Pay attention to the original. >$$\displaystyle \text{Percent change} = \frac{50}{75}\times 100 \approx 66.7\%$$. Therefore, the additional check (50) is 66.7% of the short paycheck (75). Thus, the correct answer is 67%.
Incorrect. [[snippet]] __Plug In__ 100 for the employee's initial salary. While it's true that $$\left(\frac{125-75}{\bf{100}}\right)\times 100 = 50\%$$, the question does not ask for the percent of the employee's _initial_ salary. It asks for the percent of the _short_ paycheck.
Incorrect. [[snippet]] __Plug In__ 100 for the employee's salary (the invisible variable) to demonstrate that if you decrease it by 25% ($$100-25=75$$), then a 33% check on 75 will only be about 25 ($$75\cdot 0.33 = 24.75$$). This will just get the employee back to her original salary, but her salary should have increased.
Incorrect. [[snippet]] __Plug In__ 100 for the employee's salary (the invisible variable) to demonstrate that if you decrease it by 25% ($$100-25=75$$), then a 20% check on 75 will only be 15 ($$75\cdot 0.2 = 15$$). This won't even get the employee back to her original salary—not to mention her increased salary.
20%
33%
50%
67%
80%