Chapter 7.5, Problem 23E

To determine

To answer and explain the statement.

Answer to Problem 23E

Yes, an amount can be increased by more than $100\%$ .

A $100\%$ increase represents only a doubling, so if a quantity is more than doubled, the increase is greater than $100\%$ .

Explanation of Solution

Given information:

An amount can be increased by more than $100\%$ .

Consider,

Lets take a number $100$ and increase it by $100\%$ than the result will be $200$ which is doubled the value of original number.

Net value $=$ Original value $+$ Amount of increase in value

  $\begin{array}{l}=100+100\%\times 100\left[\text{Substitute}\right]\\ =100+1.00\times 100\left[\text{Write percent as a decimal}\right]\\ =\text{200 }\left[\text{Evaluate}\text{.}\right]\end{array}$

Now consider, a quantity which is more than double of its original value to satisfy the statement,

Lets take original value be $100$ and increased value be $250$ than the increase percentp% will be,

  $\begin{array}{l}p\%=\frac{\text{Amount of increase }}{\text{Original amount}}\left[\begin{array}{l}\text{Write formula for}\\ \text{percent of increase}\text{.}\end{array}\right]\\ =\frac{250-100}{100}\left[\text{Substitute}\right]\\ =\frac{150}{100}\left[\text{Subtract}\right]\\ =1.5\left[\text{Divide}\right]\\ =150\%\left[\text{Then write decimal as percent}\right]\end{array}$

Hence,

Yes, an amount can be increased by more than $100\%$ .