Question

8.46 If 100 is decreased by a% and the result is decreased by b%, then what is the total percent decrease (in terms of a and b)? (You can assume that both a and b are between 0 and 100.)

Answer 1

Answer:

The total percent decrease is $a+b-\frac{a b}{100}$

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

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

Step 2 of 2

The percentage difference between the two percentages is,

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

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