# Stage 4 -Number – financial mathematics - successive discounts

## Strategy

Students can:

• find a percentage of a quantity
• find a percentage decrease or increase of a given quantity
• use percentages to solve problems.

## Activities to support the strategy

Students need to use their knowledge of percentages and percentage increase and decrease to solve problems involving successive percentage discounts. Students need to understand that two successive percentage discounts is not the same as a single percentage discount of the sum of the two percentage discounts. E.g. A discount of 10% followed by a discount of 5% is not the same as a single discount of 15%. Students should be made to work through both cases and see that a discount of 10% followed by a discount of 5% does not yield the same result as a single discount of 15%.

### Activity 1

1. Students should review the basic activity of percentage increase and decrease. Students may need to begin by finding the percentage of a given quantity and then subtracting it form the original. Students should then be encouraged to use the quicker method shown below.

For example:

A shop offers a 5% discount on a shirt valued at $60 50% of$60 = 0.05 × $60 =$3

$60 -$3 = $57 Students should then move on to the quicker method by realising that a discount of 5% is equivalent to finding 95% (100%–5%) of the quantity. 95% of$60 = 0.95 ×$60 =$57

2. Provide other examples which include both increase and decrease by a percentage

### Activity 2

1. Have students investigate the following situation.

• Is a discount of 10% following a discount of 5% the same as a discount of 15%?
• Determine the difference between the two discount situations?
• Have students investigate if the order of discounts is important. i.e. is a discount of 5% following a discount of 10% the same as a discount of 10% following a discount of 5%?
• The working for each case is shown below

10% discount followed by a 5% discount Straight 15% discount 5% discount followed by a 10% discount
10% discount = 90% of original
a further 5% discount
= 95% of 90%
= 0.95 x 90
= 85.5%
∴ equivalent to 14.5%
15% discount 85% of original 5% discount = 95% of original
a further 10% discount
= 90% of 95%
= 0.9 x 95
=85.5%
∴ equivalent to 14.5%

2. Provide other examples which focus on successive percentage decreases using the technique shown above. Students can be further extended by providing examples of successive increases, a decrease followed by and increase and so on

### Activity 3

Provide students with a number of real world cases of successive percentage discounts, which then extend to include a generalised process.

For example, Jim sees a TV on sale at his local store valued at \$799. It is currently on sale at 22% off. A further 5% discount is offered on the sale price if he pays cash.

If Jim chooses to pay cash, how much does he pay for the TV?

What single percentage decrease is equivalent to the successive discount of 22% and 5%?

## References

### Australian curriculum

ACMNA174: Investigate and calculate 'best buys', with and without the use of digital technologies; solve problems involving discounts, including calculating the percentage discount; evaluate special offers, such as percentage discounts, 'buy-two-get-one-free', 'buy-one-get-another-at-half-price', and so on, to determine how much is saved (Communicating, Problem Solving)

### NSW syllabus

MA4-6NA: Solves financial problems involving purchasing goods

## Student resources

• Percentage discounts - this five-page HTML resource is about solving problems concerning percentage discounts. It contains five questions and two videos. The resource discusses and explains solving problems with percentage discounts to reinforce students' understanding.
• Using percentages for expressing discounts and comparing prices - this five-page HTML resource is about solving problems concerning percentages and discounts. It contains one video and six questions, two of which are interactive. The resource discusses and explains solving problems involving percentages and discounts to reinforce students' understanding.
• TIMES Module 22: Number and Algebra: consumer arithmetic - this 23-page guide for teachers, provides an introduction to the financial mathematics component of the number and algebra strands for years 9 and 10. A brief history of the concept of money concludes the module.