Finding the Percentage Increase

In this example problem, we have three different types of number pairs. We have decimals, fractions, and dollar amounts. And what the question asks us to do is to find the percent increase for each of these pairs.

Now, the formula for finding the percent increase is going to be the same for all three pairs, but the process will be a little bit different, depending on the type of number, but I’ll demonstrate all three.

Finding the Percentage Decrease - Percentage Increase Combined LessonsTemperature rises from 60F to 72F.  what is the percent increase?
A.  
B.  
C.  
D.  
E.  
Population rises from 21,000 to 28,000. what is the percent increase?
A.  
B.  
C.  
D.  
E.  
Revenues fall from $60 million to $54 million. what is the percent decrease?
A.  
B.  
C.  
D.  
E.  
A $25 item now selling for $17.50 is discounted by what percent?
A.  
B.  
C.  
D.  
E.  
Costs change from $240 to $320.  what is the percent change?
A.  
B.  
C.  
D.  
E.  

 

Next Lesson: Percentages

The first one, we have 3.0-1.8 / 1.8, and the formula is the second minus the first over the first, and that’s going to be consistent throughout.

To solve this, we can take 3.0-1.8, which is 1.2, so we have 1.2/1.8, which is equivalent to 2/3, and the percentage form of 2/3 is 66.7%.

The second example, we have 1/4 and 2/5, so we’re going to use the same formula as here. We’re going to have 2/5-1/4 / 1/4.

Now, we have to get the common denominator here, so we’re going to multiply this first number by 4/4 to get 8/20, and the second number, we’re going to multiply by 5/5 to get 5/20.

So, what we have here is 8/20-5/20, which is equal to 3/20, and then we have to divide it by 1/4, or equivalently, what we have here is 3/20 times 4/1. Now, the 4 and the 20 cancel, dividing each by 4, we get a 1 and a 5, so what we have here is 3/5. Now, the percentage equivalent of 3/5 is 60%.

In this final example, we have dollar amounts. We have $225 and $405. So, we’ll take the final amount, 405, subtract the initial amount, 225, and divide by the initial number, $225. Now, 405-225 is 180, so what we have is 180/225.

Now, we can reduce this by dividing top and bottom by 45. 45 goes into 180 4 times, and 45 goes into 225 5 times. So, what we have is 4/5, or the percentage equivalent, which is 80%.

The next lesson: Percentages, both lessons are included in Practice Tests.