Tapping into mathematics
Tapping into mathematics

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Tapping into mathematics

5.4 Percentage increases and decreases

There is no single right way of calculating percentage increases or decreases. The next examples show two different approaches to the same problems.

Example 1

A railway season ticket from my local station to London costs (at current prices) £825. Calculate the cost of a new ticket, if prices have risen by 6%.

Method 1

To find the cost of a new ticket, you can find 6% of £825 and then add this amount on to the original cost. Remember that a given percentage is simply a fraction made up of that number divided by 100. So 6% is 6/100.

A 6% rise means a fare increase of £825 × 6/100 = £49.50

So the new cost of a season ticket is £825 + £49.50 = £874.50.

One way of doing this on the TI-84 calculator is:

  • set the calculator to display 2 decimal places

  • Input 825 6 100

  • Input 825

Method 2

This is a more elegant method. The original cost of £825 was 100%. So increasing it by 6% will give 106%. Hence work out 106% of £825. However 106% is 106/100 or 1.06. So an elegant calculation of the new fare is £825 × 1.06. Your calculator should give the new value of 825 ×1.06 = 874.50. So the cost is £874.50.

Example 2

When I went to the local branch of a department store, I was offered 15% off the price of whatever I bought, if I signed up for the company's credit card. My purchases came to £74.64. What would the price be if I took up the company's offer?

Method 1

15% of 74.64 = 15/100 × 74.64 = 11.20 (to 2 d.p.)

So reduction is £11.20.

The new price in £ is 74.65 − 11.20 = 63.44

So I would pay £63.44.

Method 2

The original price of £74.64 is 100% and so reducing the price by 15% will give 100% – 15% or 85% of the original price. Now 85% is 85/100 or .85. So the new price in is: 0.85 × .74.64 = 63.44 (to 2 d.p.)

Hence I would pay £63.44, if I took the company's offer.

The next exercise will give you some more practice at calculating percentage increases and decreases.

Exercise 6: Ups and downs

Practice calculating percentage changes by completing the table below. In the last line of the table you will see a line over a number: this means recurring (33.3333333333… or one third).

Original price Percentage price Final price
£100 77% increase £177.00
£2750 11% decrease £2447.50
£100 18% decrease
£1080 35% increase
£51 100% increase
£2 250% increase
£3 33.% decrease

Answer

Original price Percentage price Final price
£100 77% increase £177.00
£2750 11% decrease £2447.50
£100 18% decrease £82.00
£1080 35% increase £1458.00
£51 100% increase £102.00
£2 250% increase £7.00
£3 33. % decrease £2.00
MU120_4MCAL

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