Question

A 23% increase followed by a 17% decrease is what percent change?

Answer 1

Answer: 2.09% increase

Explanation:

Let x = the original amount. then

23% increase is: x(1 + 0.23) = 1.23x

and a 17% decrease is 1.23x(1 - 0.17)

= 1.23x(0.83)

= 1.0209x

x was the original amount and 1.0209x is the new amount.

The percent change is:
`(new-original)/(original)=(1.0209x-x)/(x)=(0.0209x)/(x)=0.0209`

Since the result is positive, it represents an increase.

Move the decimal two places to the right to convert the number to percent.

+0.0209 = 2.09 increase

Answer 2

A 2.09% increase.

This is just some simple multiplication. A 23% increase is the same as multiplying by 1.23, and a 17% decrease is like multiplying by 0.83, since 100-17=83. Just multiply 1.23*0.83, which equals 1.0209, or a 2.09% increase.