Percentages
20 Change as a Percent and Percent Change
Expressing Change as a Percent
Melissa is a carpentry foundation student who has just finished her six-month foundation program. This is a program for people who are looking to get into the trade but are not yet apprentices.
It’s now time to make some money after spending the previous six months in school. After Melissa graduated from the program, she applied for three jobs and decided to take the one that offered the best value. Her starting wage is $14 per hour, and after six months, it will move up to $16 per hour.
This is a $2 per hour pay raise, but does this represent a good percentage increase? If she started at $25 per hour and went up to $27 per hour, would this be the same percentage increase?
The answer lies in the following formula:
[latex]\text{Percentage change}=\dfrac{\text{Actual increase or decrease}}{\text{Original amount}}\times100[/latex]
There are a couple of things to note here. One is that this formula works if you have either an increase or a decrease from the original amount. If Melissa’s wage went down, you could also express that as a percentage. The second thing to note is that there is the number 100 at the end of the formula. This is due to the fact that the calculation would give us a decimal, and multiplying this number by 100 makes it a percentage.
So, to follow through on our calculation, let’s put the numbers in and see what we get.
[latex]\LARGE\text{Percentage change}=\dfrac{\$2}{\$14}\times100[/latex]
[latex]\LARGE\text{Percentage change}=0.1429\times100[/latex]
[latex]\LARGE\text{Percentage change}=14.29\%[/latex]
This is telling us that Melissa will get a 14.29% increase in her wage after the first six months. Not bad!
Example
During her foundation program, Melissa had to keep her job working at a coffee shop in order to pay the bills. On her first day of work, she served 78 cups of coffee. During her six months on the job, the most cups of coffee she made in one day was 201. How can the difference between these amounts be expressed as a percentage increase?
Step 1: Calculate the increase in cups served.
[latex]\LARGE201-78=\text{123 more cups of coffee}[/latex]
Step 2: Write down the formula you are going to work with.
[latex]\text{Percentage change}=\dfrac{\text{Actual increase or decrease}}{\text{Original amount}}\times100[/latex]
Step 3: Plug the numbers into the formula.
[latex]\LARGE\text{Percentage change}=\dfrac{123}{78}\times100[/latex]
Step 4: Work through the answer.
[latex]\LARGE\text{Percentage change}=1.58\times100[/latex]
[latex]\LARGE\text{Percentage change}=158\%[/latex]
This answer tells us that, from the time Melissa started to the time she had her most productive day, she had a one-day increase of 158%. If she were to increase her output by 100%, that would mean mathematically that she would be making twice as much coffee as before. Increasing by 158% indicates that she is making MORE than twice the amount of coffee as when she first