Price Change and New Price in Two Steps

Percentages are used very often in daily life. A shop might have a sale—for example, they’re offering a $30$ % discount)—or the price of a bus ticket might be increased by $6$ %.

Let’s begin by practicing how to find the new price without thinking about percentages:

Rule

DiscountandPriceIncrease

New price = Old price - discount

New price = Old price + price increase

I will deal with discounts given as a percentage first.

Example 1

A jacket used to cost $\text{}\text{}250\text{}$, but it is now being sold at a $\text{}20\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ discount. What is the current price of the jacket?

You can figure out the answer in two steps:

The discount is $\begin{array}{llll}\hfill 20\phantom{\rule{0.17em}{0ex}}\text{%}×\text{}250& =20×\frac{1}{100}×\text{}250\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}50\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

That helps give you the new price:

At other times, the price might be increasing by a given percentage. You find this new price in a similar way, you just have to add instead of subtracting.

Example 2

A monthly bus ticket used to cost $\text{}\text{}32\text{}$, but then the price increased by $\text{}15\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$. What is the new price?

You can do this in two steps the following way:

The increase in price is $\begin{array}{llll}\hfill 15\phantom{\rule{0.17em}{0ex}}\text{%}×\text{}32& =\frac{15}{100}×\text{}32\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}\frac{15×32}{100}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\text{}4.80\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

The new price is: $\text{}32+\text{}4.80=\text{}36.80$