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: a+b-ab/100 hope this is right

Answer 2

The total percent decrease is
`$a+b-(a b)/(100)$`

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

`$$\begin{aligned}(b)/(100) *(100-a) &=(100 b-a b)/(100) \\(100 b)/(100)-(a b)/(100) &=b-(a b)/(100)\end{aligned}$$`

Step 2 of 2

The percentage difference between the two percentages is,

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

Since 100 is the total percent
`$a+b-(a b)/(100)$` is the percentage decrease.