Increased by is similar to decreased by in that we have a choice of solving the problem in two steps or just one step. The difference is that with increased by we are beginning with the whole amount (100%) and then increasing that amount by an additional amount. This means that instead of subtracting we add the amount indicated by the percentage.
Example: What is your new salary if your current salary of $24,000 is increased by 3.5%?
Two steps: Find 3.5% of $24,000.
0.035($24,000) = $840.
Then old salary + increase = new salary.
$24,000 + $840 = $24,840.
The new salary is $24,840.
Your new salary is 100% of your current salary plus 3.5% of your current salary. This means that your new salary is (100% + 3.5%) = 103.5% of your current salary. So we work the problem in one step by finding 103.5% of your current salary.
One step: Find 103.5% of 24,000.
1.035($24,000) = $24,840.
The new salary is $24,840.
Notice in the example above that to solve the increased by problem in one step, we work with a percent that is greater than 100%. This makes sense because we are getting 100% of our current salary PLUS the increase.
Sam owns stock in MDV. Sam heard on the news that a share of MDV stock increased by 4.2% today but missed hearing today's price. Sam remembers that the closing price yesterday was 83.5. What was today's closing price?
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Date last modified: July 19, 2010.
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By Kris Montis and Timothy Peil
