When buying products, two things that are important to understand are mark ups and discounts.
A mark up is a percentage increase in the price of a product.
A discount is a percentage decrease in the price of a product.
A mark up indicates that the price of the product has increased from its original price and the percentage of the mark up indicates by how much. For example: if the price of a jumper has been marked up by $20%$20%, then its price has been increased by $20%$20%.
Similarly, the percentage of a discount indicates how much the price of a product has decreased from its original price.
Since mark ups and discounts are simply percentage increases and decreases, we can calculate them using the same methods.
An encyclopedia priced at $\$110$$110 is marked up by $40%$40%. What is the marked up price of the encyclopedia?
Think: We are given that the original price of the encyclopedia is $\$110$$110. Since it has been marked up, we are calculating a percentage increase. The amount that we are increasing by is $40%$40%.
Do: To increase the original price by $40%$40%, we multiply it by $140%$140%. This gives us:
Marked up price = $140%\times110$140%×110
Evaluating the expression tells us that the marked up price is $\$154$$154.
A pair of boots priced at $\$80$$80 is discounted by $35%$35%. What is the discounted price of the pair of boots?
Suppose a video game was marked up by $20%$20%, later discounted by $25%$25% and finally discounted again by $40%$40%. If the original price of the video game was $\$50$$50, what is its current price?
If we calculate the changing price of the video game through each mark up and discount we find that:
As such, we find that the current price of the game is $\$27$$27.
However, this is a lot of steps. Notice that the only operation we applied to the price was multiplication. Since multiplication does not need to be applied one at a time, we can reach the same answer by calculating:
Current price = $\$50\times120%\times75%\times60%$$50×120%×75%×60%
The advantages of this approach are that we can cancel out factors if we convert the percentages into fractions, or simply use a calculator to evaluate the expression in one step. Since the order in which we multiply doesn't matter either, we can also choose which percentage changes we want to apply first to make calculations easier.
Mark ups and discounts of the same percentage do not cancel each other out.
For example: if an item is marked up by $10%$10% and then discounted by $10%$10%, its final price will be:
Final Price = Original Price $\times$× $110%\times90%$110%×90%
Evaluating the left hand side, we get:
Final Price = Original Price $\times$× $99%$99%
As we can see, the final price and the original price are not the same.
A hula hoop priced at $\$10$$10 is marked up by $40%$40% and then later discounted by $40%$40%.
Which of these expressions is equal to the new price?
Calculate the new price of the hula hoop.
Give your answer in dollars, to the nearest cent.
Which of the following is true?
A bladesmith began her career selling her swords for $\$1500$$1500. After a few months she marked up the price by $16%$16%.
A few weeks after that a video of her making the swords went viral, and she marked up the price by $11%$11%.
In a few days she is due to appear on a popular podcast, and in anticipation of the increased demand she marks up the price by $13%$13%.
What is the price of the bladesmith's swords after all the mark ups?
Give your answer in dollars, to the nearest cent.
Almost everything we buy has a compulsory $10%$10% mark-up applied to it, called goods and services tax (GST). The extra money we pay goes to the government, and they can spend it on essential things like schools and roads. Some items we buy are excluded from GST. The most common examples are fresh fruit and vegetables, as well as other basic foods such as bread, flour, oil, and dairy products.
We can calculate the total price, inclusive of GST, in the same way we calculate percentage increases.
GST is a $10%$10% price increase.
A book has a pre-GST price of $\$20$$20. Find the price of the book, inclusive of GST.
Think: GST is $10%$10% and it increases the price. So we need to calculate a $10%$10% increase in the pre-GST price of the book.
Do: To increase the price by $10%$10%, we multiply by $110%$110%. This gives us:
|Price including GST||$=$=||$110%\times20$110%×20|
The total price a customer needs to pay for the book is $\$22$$22.
A computer has a price including GST of $\$1265$$1265. Find the pre-GST price of the computer.
Think: We have been given the price including GST which is the same as being given the final price after a $10%$10% increase. To find the pre-GST price we can modify the formula:
|Original price$\times$×$110%$110%||$=$=||Final price||
|Original price||$=$=||Final price$\div$÷$110%$110%||
Dividing by $110%$110%
Do: To find the pre-GST price we can divide by price including GST by $110%$110%.
The pre-GST price of the computer is $\$1150$$1150.
Reflect: The pre-GST price is not just the price including GST decreased by $10%$10%. This is because, as we saw earlier, percentage increases and decreases do not cancel each other out.
A board game has a pre-GST price of $\$30$$30. Find the price of the board game inclusive of GST.
A book has a price including GST of $\$55$$55. Find the pre-GST price of the book.
operates with fractions, decimals and percentages
solves financial problems involving purchasing goods