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

Discount and Price Increase

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 $$ 250$ , but it is now being sold at a $20 %$ discount. What is the current price of the jacket?

You can figure out the answer in two steps:

The discount is

\begin{array}{l} 20 % \times $ 250 & = 20 \times \frac{1}{100} \times $ 250 \\ = $ 50 \end{array}

That helps give you the new price:

\begin{array}{l} Old price - discount & = $ 250 - $ 50 \\ = $ 2005 \end{array}

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 $$ 32$ , but then the price increased by $15 %$ . What is the new price?

You can do this in two steps the following way:

The increase in price is

\begin{array}{l} 15 % \times $ 32 & = \frac{15}{100} \times $ 32 \\ = $ \frac{15 \times 32}{100} \\ = $ 4.80 \end{array}

The new price is: $$ 32 + $ 4.80 = $ 36.80$

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Activities 2

Finding Price Changes in One Step