50.5k views
4 votes
A number is decreased by 50%, and the result is increased by 50% to get99. What is the original number? *

User Jan Wy
by
3.5k points

1 Answer

7 votes

Let the original number be


=x

The number decreased by 50% means that we will first calculate 50% of the original number and then subtract it from the original number x


\begin{gathered} 50\text{ \% of the original number will give} \\ =50\text{ \% of x} \\ =(50)/(100)* x=0.5x \end{gathered}

Then, let's subtract the decreased value from the original value

The remaining value will be


\begin{gathered} \text{remaining value} \\ =x-0.5x \\ =0.5x \end{gathered}

The result is increased by 50% to get


\begin{gathered} increasedvalue=50\text{ \% of the remaining value} \\ =(50)/(100)*0.5x \\ =0.5*0.5x \\ =0.25x \end{gathered}

The new value after increasing by 50 % can be gotten by adding the increased value to the remaining value


\begin{gathered} \text{the new value will be} \\ =0.5x+0.25x \\ =0.75x \end{gathered}

From the question, the new value =99

Therefore, the original value will be


\begin{gathered} 0.75x=99 \\ \text{divide both sides by 0.75} \\ (0.75x)/(0,75)=(99)/(0.75) \\ x=132 \end{gathered}

Hence,

The original number = 132

User PVCS
by
4.0k points