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Welcome to our Math lesson on Percentage Change, this is the first 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.
Imagine you were paid $16/hour and got a $3/hour salary increase. Obviously, now you earn $19/hour. How do you respond to somebody who asks you what percent your salary increased by?
It is clear that you have to express the change in salary as a percentage. For this, we use the general formula
where x is the original value while Δx = xfinal - xinitial (initial = original) is the difference between final and initial value of the quantity involved in the study.
The change Δx may be positive or negative. If it is positive, then the final value is greater than the initial one. In this case, we have a percentage increase; otherwise, if the final value is smaller than the initial (original) one, we have a percentage decrease, We will discuss percentage increase and percentage decrease extensively in the following paragraphs.
In our example, we have an increase in salary by $3 (Δx = $3), so we don't need to know the initial and final values, as we already have the change (increase) provided. In addition, we know that the original value is x = $16. Thus, applying the formula above, yields
Although $3 may seem a small amount of daily salary increase, it is actually high when considered against the original daily salary. Therefore, knowing the net increase or decrease of an amount is not always sufficient to draw a conclusion on how the situation changes. Let's consider an example to clarify this point.
Two friends, Sam and Jack had a simultaneous increase in salary while working for two different companies. Sam had an increase of $3/hour while Jack had an increase of $4/hour. Sam was original paid by $15/hour while Jack was paid by $22/hour. Who had a higher percentage of salary increase? Write the answers at three significant figures.
We denote the values related to Sam by x and those related to Jack by y. Therefore, we have
Thus, applying the formula of percentage change, we obtain for the percentage of salary increase for Sam:
On the other hand, the percentage increase in salary for Jack is
Therefore, despite Jack receiving a higher net increase in salary than Sam ($4 > $3), Jack had a higher percentage increase in salary than Sam (20.0% > 18.8%).
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