This section illustrates one strategy for finding ‘original’ prices from discounted and marked-up prices. Using a double number line can help learners visualise how to get to the answer, and gives them a problem-solving tool for percentages that they can use in other contexts. This teaching approach helps learners build number sense.
Pre-Discount Price
Often we see sale prices advertised after a percentage discount has been taken off. How do we work out what the original price was?
The sale price is $960, how can we work out what the original price was?
The original price is always 100% or the whole.
The sale price is 85% of the original price (100% - 15%).
Use what you know about 85% to find 1%
$960 represents 85%; so if we divide 960 by 85 we find the value of 1% is $11.29.
Use 1% to find 100%
To find 100%, we multiply the value of 1% by 100. This gives the original price.
Summarise the problem
$960 ÷ 85 = 11.29 or 1%.
$11.29 x 100 = $1129 or 100%
$1129.00 is the original price.
Ask your learners how the working would change if the discount was 25% or 30%. Get them to try and generalise the steps for any percentage discount.
Pre-Marked Up (Wholesale) Price
A business shirt retails for $159.90 (excluding GST) after a 30% mark-up. What is the wholesale price (price before the mark-up)?
Again, we’re looking for the original (wholesale) price which is 100%, but in this example we are given a marked up price which represents 130% of the wholesale price.
Use what you know about 130% to find 1%
$159.90 represents 130%; so if we divide 159.90 by 130 we find the value of 1% is $1.23.
Use 1% to find 100%
1% is $1.23, so multiply by 100 get the wholesale price (100%).
Summarise the problem
159.90 ÷ 130 = $1.23 or 1%
$1.23 x 100 = $123.00 or 100% (Wholesale Price)
Ask your learners how the working would change if the mark-up was 25% or 40%. What about a mark-up of 125%? Get them to try and generalise the steps for any percentage mark-up.
Key numeracy outcomes
This teaching sequence helps learners to:
- Solve problems using proportional thinking
- Develop formulae that they understand
- Develop understanding of percentages