Respuesta :

Answer:

The total percent decrease is [tex]$a+b-\frac{a b}{100}$[/tex]

Step-by-step explanation:

  • We are given with a word problem
  • We are asked to find the total percentage decrease
  • We can do this in two steps

         Step 1: Finding the two percentage decrease

         Step 2: Finding their difference

Step 1 of 2

Let the decrease by a% be 100-a

Then b% decrease is

[tex]$\begin{aligned}\frac{b}{100} \times(100-a) &=\frac{100 b-a b}{100} \\\frac{100 b}{100}-\frac{a b}{100} &=b-\frac{a b}{100}\end{aligned}$[/tex]

Step 2 of 2

The percentage difference between the two percentages is,

[tex]$\begin{aligned}&(100-a)-\left(b-\frac{a b}{100}\right)=100-a-b+\frac{a b}{100} \\&100-a-b+\frac{a b}{100}=100-\left(a+b-\frac{a b}{100}\right)\end{aligned}$[/tex]

Since 100 is the total percent [tex]$a+b-\frac{a b}{100}$[/tex] is the percentage decrease.

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