Question

percents build on another in strange ways.it would seem that if you increased a number by 5% and then increased its result by 5%more , the overall increase would be 10% (a) increase 100 by 5%(b)increase your result form (a)by 5%(c)what was the overall percent increase of the number 100? why is not 10%

Answer 1

Step-by-step explanation:

a) increase 100 by 5%

`\begin{gathered} 105\text{\% of 100 = 1.05}*100 \\ =105 \end{gathered}`

b) increase your result form (a)by 5%

`\begin{gathered} 105\text{\% of 105 = 1.05}*105 \\ =110.25 \end{gathered}`

c) The overall percent increase of the number 100;

`\begin{gathered} \text{ \%P = }(110.25-100)/(100)*100\text{\%} \\ \text{ \%P= 10.25\%} \end{gathered}`

It is not 10% because the second 5% increase was not on the initial number 100.

increasing 105 by 5% is more than increasing 100 by 5%.

Therefore, increasing 100 by 5% followed by increasing the result by 5% is greater than increasing 100 by 10%.