We use the percentage to increase (increase or inflation) or decrease (decrease, deflate or discount) and the symbol we use to represent it is the % (percent).
When a certain value is increased or decreased for more than one consecutive time, we can calculate the percentage composition. So we have problems related to percentage composition are resolved through the product of the multiplication factor.
This factor is different for increase or decrease. In addition, we must add 1 to the amount referring to the rate of increase; in the decrease, we have to subtract 1 from the discount rate.
Example: Multiplicative factor for addition:
A product increased 20%. What is the multiplication factor that represents this increase?
Reply
Increase rate: 20% = 20 = 0,20 = 0,2
100
Multiplication factor = 1 + rate of increase
Multiplication factor = 1 + 0.2
Multiplication factor = 1.2
Example: Multiplicative factor for decrease:
A product received a 20% discount. What is the multiplication factor that represents this decrease?
Discount rate: 20% = 20 = 0,20 = 0,2
100
Multiplication factor = 1 - discount rate
Multiplication factor = 1 - 0.2
Multiplication factor = 0.8
Now that we know how to calculate the multiplication factor, let's solve two problems that have the calculation of percentage composition.
first problem
Find the rate of increase by calculating the percentage composition, of a product that had an increase of 30% and then another increase of 45%.
Reply:
We must calculate the multiplication factor referring to 30% and 45%.
Increase rate 30% = 30 = 0,3
100
Increase rate 45% = 45 = 0,45
100
Multiplication factor for 30% = 1 + 0.3
Multiplication factor for 30% = 1.3
Multiplication factor for 45% = 1 + 0.45
Multiplication factor for 45% = 1.45
Calculation of percentage composition = 1.3 x 1.45 = 1.885
To know the rate of increase that is built into the value of the percentage composition, Knife:
1.885 = 1 + 0.885 = 1 + rate of increase
Increase rate = 0.885 x 100 = 88.5%
second problem
Find the shrinkage rate, by calculating the percentage composition, of a product that experienced a 25% increase, followed by a 50% decrease.
Reply:
Increase rate = 25% = 25 = 0,25
100
Decrease/discount rate = 50% = 50 = 0,5
100
Multiplication factor for 25% = 1 + 0.25
Multiplication factor for 25% = 1.25
Multiplication factor for 50% = 1 - 0.5
Multiplication factor for 50% = 0.5
Calculation of percentage composition = 1.25 x 0.5 = 0.625
To know the rate of decrease that is in the value of the percentage composition, Knife:
1 - 0.625 = 0.375, where 0.375
Decrease rate = 0.375 x 100 = 37.5%
third problem
A product suffers inflation in January of 15% and in February, 20%. What is the total inflation in these two months?
Reply:
In early January the product cost x reais. In early February it cost x reais plus 15% of x. We can build an equation with this information.
first equation
First rate of increase = 15% = 0.15
y = x + 0.15x
y = 1.15x
We must build another equation, we will get it thinking about the cost of this product in early March.
Second rate of increase = 20% = 0.2
z = y + 0.2y
z = 1.2y
We obtain the following equations:
y = 1.15x
z = 1.2y
By the equation replacement method, we have to:
z = 1.2y
z = 1.2. 1.15x
z = 1.38x
We have that 1.38 is the multiplication factor. As inflation is a rate of increase/inflation, to obtain it do:
1.38 = 1 + 0.38 = 1 + rate of increase
Rate of increase/inflation = 0.38 x 100 = 38%
The final answer to this question is: The total inflation of this product was 38%.
By Naysa Oliveira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/calculo-composicao-porcentagem.htm
