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Calculating percentage discount

We often see percentage used when items at the shops are sold cheaper than the original price. We call this a percentage discount.

Example 2

A pair of jeans is sold at 30% discount. If the original price is $110, what is the price after the discount has been applied?

Solution method 1

To calculate the price after a discount has been applied we calculate the percentage and subtract it from the original price.

\begin{align}30\%\ \text{of}\ 110&=\dfrac{30}{100}×110\\\\ &=\dfrac{3}{10}×\dfrac{110}{1}\\\\ &=\dfrac{3}{1}×\dfrac{11}{1}\\\\ &=33\end{align}

So the discount is $33. We subtract $33 from $110 to get the final price of $77.

Solution method 2

Using the unitary method:

\begin{align}10\%\ \text{of}\ 110&=\$11\\\\ \text{So}\ 30\%\ \text{of}\ 110&=3 × 11\\\\ &=33\\\\ 110\ –\ 33&=77\end{align}

The customer pays $77.

Solution method 3

Another way to calculate the price after the discount is applied is to work out the percentage that remains. So a 30% discount is the same as paying 70% of the original price.

\begin{align}70\%\ \text{of}\ 110&=\dfrac{70}{100}×110\\\\ &=\dfrac{70}{100}×\dfrac{110}{1}\\\\ &=\dfrac{7}{1}×\dfrac{11}{1}\\\\ &=77\end{align}

So the customer pays $77.

Solution method 4

Using the unitary method:

\begin{align}10\%\ \text{of}\ 110&=11\\\\ \text{So}\ 70\%\ \text{of}\ 110&=77\end{align}

So the customer pays $77.