Chapter 11

Chapter 11 (percentages)

                                     

In this chapter you will learn more about percentages.

11.1 Using mental method

Some percentages are easy to find because they are simple fractions. But some of them are hard to find because they are not always a simple fraction.

Example

Question

26% of 78 = 20.28

Use this fact to find:

    A)52% of $78 B) 13% of 78 kg C) 65% of 78 km

D) 104% of 78 million

Answer

    A) 20.28 × 2 = 40.56 B) 20.28 ÷ 2 = 10.14 C)

D) 20.28 × 4 = 81.14

Question

à Work out:

    A) 12.5% of 80  B) 0.5% of 7000 C) 150% of 62

D) 125% of 260 E) 110% of 36

à Work out:

    A) 35% of 84 B) 49% of 230 C) 77% of 4400

D) 99% of 7900 E) 45% of 56000

11.2 comparing different quantities

You will often need to compare groups that are different sizes.

Example

Question

This table shows the results of a survey in a factory.

	SMOKER	NON-SMOKER	TOTAL
MEN	12	64	76
WOMEN	9	32	41

    A) What percentage of men are smokers?

    B)  Compare the percentages of men and women who are non-smokers

Answer

A) 12/76 × 100% =  15,78 %

B)  Men : 64/76 × 100 % = 84,21 %

Women: 32/41 × 100% = 78,04 %

Question

 Ø There were 270 people in cinema. There were 168 women and 102 men.

There were 152 people in a theatre. There were 78 women and 74 men.

    A) Work out the percentage of women in each venue.

    B)  Work out the percentage of men in each venue.

Answer

    A) 113,3

    B)  86,3

11.3 percentages changes

You can use percentages to describe a change in a quantity. It could be an INCREASE or a DECREASE.

Question

 Ø The price of a car was $ 20.000. In a sale, the price decreased by 4%. After the sale it increased by 4%

A) What mistake has Ahmad made?

B)  What is the correct price after the sale?

Ahmad said” the price after the sale is % 20.000 again”

Answer

A)  Estimating the sale price

B)  4%4= 4/100 ×  $20 000 = 800

= 20 000 – 800 = 19 200

Price after sale = 4/100 x 19 200 = 768

                        = 19 200 + 768

11.4 Practical examples100 x $20 0

Profit: sell for more than you buy

Loss: sell for less than you buy

Discount: reduction in the price, it is usually given as a percentage

Interest: bank charges

Tax: if you buy something the price may include a additional price.

Examples

Question

 Ø A women bought an old chair for $240. She sold it for $ 300

Work out the percentages profit.

 Ø  A man bought a car for $ 15 900. He sold it for

$9500

Work out the percentages loss.

 Ø  A bottle of juice costs $ 6.50

If you buy six bottle you can get 10% discount.

Work out how much he sells them for.

Answer

 Ø  $ 300 - $ 240 = 60

60/240 x 100 % = 25 %

 Ø  15 900 – 9500 = 6400

6400/15900 x 100% = 40, 25 %

 Ø  6 x 6.5 = 39

Discount = 10/100 x 39 = 3, 9

After discount = 39 – 3, 9 = 35, 1

39-35, 1 = 3.9

00 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 7684% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 7684% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 7684% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 7684% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
               4% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 768