Percentage changes

© Boardworks Ltd 20091 of 11

This icon indicates the slide contains activities created in Flash. These activities are not editable.

This icon indicates an accompanying worksheet.This icon indicates teacher’s notes in the Notes field.

If you have any questions about the Boardworks Maths customer club, or queries about your Boardworks software, please don’t hesitate to contact your account manager on

08703 50 55 60.

© Boardworks Ltd 20092 of 11

Spring 2010 exclusive customer content

using percentages

interpreting decimals and percentages as operators.

This presentation has been developed for use with the new GCSE exam specifications for 2010 and covers:

This presentation looks particularly at how to calculate percentage increases, decreases and reverse percentages.

It also looks at how the changes to the VAT rate from 1st January 2010 will impact on the cost of items and services.

© Boardworks Ltd 20093 of 11

Percentage increase

© Boardworks Ltd 20094 of 11

An antique lamp, bought 20 years ago for £50, has increased in value by 60%. How much does it now cost?

160% × £50

= 1.6 × £50

Percentage increase

A jacket costs £86 before VAT (17.5%) is added. What is the total cost of the jacket?

117.5% × £86

= 1.175 × £86

= £80

= £101.05

© Boardworks Ltd 20095 of 11

Console price difference

Neil was shopping in town and spotted deals in two different shops on a games console.

Which is the better deal and by how much?

If Gametastic offered this price in December 2009, when VAT was 15%, how much cheaper would it have been?

How much would Gametastic have to reduce their advertised price by to be cheaper than Games R Us?

Gametastic: £174 + VAT (17.5%)

Games R Us: £199.99 (incl. VAT)

© Boardworks Ltd 20096 of 11

Percentage increase

On 1 January 2010 the VAT rate on goods and services increased from 15% to 17.5%.

How much more expensive are these bills now than they would have been if the work was done before January 1st?

Fitting taps

£70 + VATWaste pipe

replacement

£145 + VAT

New bath

and fittings

£1950 + VAT

Victorian sink

and taps

£2445 + VAT

Mr Smith had the following work done in his bathroom at the beginning of January.

© Boardworks Ltd 20097 of 11

Percentage decrease

© Boardworks Ltd 20098 of 11

Percentage decrease

© Boardworks Ltd 20099 of 11

Reverse percentages

Sometimes, the price after a percentage increase or decrease is given and the original amount is to be calculated.

What was the original price?

This can be solved using inverse operations.

Let p be the original price of the jeans.

p × 0.85 = £25.50 so p = £25.50 ÷ 0.85 = £30

price before discount

× 0.85%price after discount

÷ 0.85%

These jeans were bought in a sale. They had 15% off and cost £25.50.

© Boardworks Ltd 200910 of 11

Reverse percentages

© Boardworks Ltd 200911 of 11

Reverse percentages

What is the cost beforeVAT is included?

What would the cost have been, including VAT, if thesystem had been purchased before 1 January 2010?

The panels reduce the £790 heating bills by 85% per year.How long will it be before the system has paid for itself?

The cost of a solar panel system to heat a house, including VAT at 17.5%, is £8812.50.