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Welcome to our Math lesson on Percentage Increase, this is the second lesson of our suite of math lessons covering the topic of Percentage Increase and Decrease, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Now, let's focus on percentage increase and start with a mind blowing example:
An employee has excellent performance in his work, so the boss decided to triple his salary. By how what percent did the employee's salary increase?
I am sure many people will respond immediately: "The employee's salary increased by 300% since the boss tripled his previous salary." Although this may seem reasonable, it is a wrong answer because the term "triples" means three times the original value. Therefore, if we express the initial salary by S, the actual salary after the increase becomes 3S. Therefore, the increase in salary, which represents the difference between the current and the previous salary is obtained through subtraction, i.e.
Therefore, since S represents 100% of the previous salary, we have a percentage increase by
and not 300% as you may initially have thought.
In this way, we may induce the formula of percentage increase, that is
If the old and the new percentage (i.e. initial and actual) of an amount are known, the percentage increase is obtained through the formula
or
The number of bacteria in a sample of contaminated water increased from 2,000 to 15,000 in one day. What is the percentage increase of the bacteria?
Clues:
Thus, we have
As we stated earlier, we can also work out the percentage increase by taking the initial value as 100% and finding the actual value in terms of the initial value as percentage (100%). Then, the initial percentage is subtracted from the actual, in order to obtain the percentage increase. Thus, in the previous example, we may express the actual number of bacteria in terms of 100% (the initial value), i.e.
Thus, applying the ratio approach, we obtain
Taking the cross product, we obtain
Therefore, the percentage increase is
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