Question

The price of an item that sold for $480 was reduced by 25%. By what percent must the price of the item be increased to bring the price back to $480

Answer 1

When an item is reduced by a certain amount in percentages, the new value is equal to 100% subtracted by the given percentage. In this case the item had its price reduced by 25%, so the new value would be:

`100\text{ \%}-25\text{ \%}=75\text{ \%}`

The value after the reduction is 75% of the original one. We can calculate this value as shown below:

`\begin{gathered} \text{ new value}=(75)/(100)\cdot480 \\ \text{ new value}=0.75\cdot480=360 \end{gathered}`

The new value is $360. We need to find the percentage increase value that will make it equal to $480 again. To do that we need to do as shown below:

`\begin{gathered} 480=x\cdot360 \\ x=(480)/(360)=1+0.33333 \\ x=100\text{ \% }+(33.3333)/(100) \\ x=100\text{ \% + 33\%} \end{gathered}`

The increase in value must be equal to approximately 33.33%.