11.4 Practical Examples

Here are some real-life examples of uses of percentages.

• If you buy something and sell it, the difference between the two prices is a profit or a loss. It's given as a percentage of the buying price. If you buy something for $20 and sell it for $15 you make a loss of $5 or 25%.
• When you buy something you may be offered a discount. This is a reduction in the price. It's usually given as a percentage. If the price is normally $20 and you get a 10% discount, you only pay $18.
• If a bank helps you to buy an item, you may have to pay back more than you borrow. This is the interest that the bank charges. It's given as a percentage of the cost. If a car costs $20000 and the rate of interest is 3%, you will pay $20600.
• If you buy something the price may include a tax. This is called a purchase tax. When you earn money you may have to pay tax on what you earn. This is called income tax.

I have three questions to ease your understanding.

Questions

1. A woman bought an old chair for $240. She sold it for $300. Work out the percentage profit.

Profit: 300 - 240 = 60. 60/240*100% = 25%

2. A man bought a car for $15900. He sold it for $9500. Work out the percentage loss.

Loss: 15900 - 9500 = 6400. 6400/15900*100% = 40%

3. A bottle of grape juice costs $6.50. If you buy six bottles you can get 10% discount. Work out how much you save if you buy six bottles. 

=> 6.50*6 = 39. 39*90% = 35,10.

39 - 35,10 = $3,9

11.3 Percentage Changes

You can use percentages to describe a change in a quantity. It could be a decrease or an increase. A percentage is always calculated as a percentage of the initial value. The initial value is 100%. It's important to choose the correct value to be 100%. I have three questions to ease your understanding.

Question

1. Here are the prices of three items in Alain's shop.
Game $40   Phone $120  Computer $500
Alain increases all the prices by $10. Find the percentage increase for each item.

Game: The initial value is 40. So 10/40*100% = 25%
Phone: The initial value is 120. So 10/120*100% = 8,3%
Computer: The initial value is 500. So 10/500*100%

2. These are the masses of three children on April.
Luke 6kg   Bridget 14kg   Thomas 25kg
Over a year, the mass of each of them increased by 10%. Work out the new mass of each child.

Luke: 6*110% = 6,6 
Bridget: 14*110% = 15,4
Thomas: 25*110% = 27,5

3. The price of a car was $20000. In a sale, the price decreased by 4%. After the sale it increased by 4%.
Ahmad says "The price after the sale is 20000 again"
a. What mistake has Ahmad made?
b. What is the correct price after the sale?

a) He misplace the initial value for the price after sale. The first initial value is 20000. the second initial value is 19200. So the result won't be the same as before.

b) 19200*104% = 19968

11.2 Comparing Different Quantities

You will often need to compare groups that are different sizes.
In this case, it'll be easy if you use percentages.

                                  
I have three questions to ease your understanding.

Questions

1. There were 270 people in cinema. There were 168 women and 102 men. There were 152 people in a theatre. Theatre 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.

a) cinema: 168/270*100% = 62%
    theatre: 78/152*100% = 51%

b) cinema: 102/270*100% = 37%
     theatre: 74//152*100% = 49%

2. In Alphatown there are 5400 young people aged 18 or less. There are 9300 aged over 18. in Betatown there are 9300 young people aged 18 or less. There are 21600 aged over 18.

a. Calculate the percentage of young people in each town.
b. Which town has the greater proportion of young people?

a)
 Alphatown:  5400/14700*100% = 37% {5400 is the amount of young people, 14700 is the amount of all people.}
Betatown: 9300/30900*100% = 30%

b) Alphatown: 37%
    Betatown:  30%

= Alphatown.

3. This table shows the result of a survey in a factory.

a. What percentage of men are smokers?
b. Compare the percentages of men and women who are non-smokers.

a) 12/76*100% = 16%
b) Men: 64/76*100% = 84%
    Women: 32/41*100% = 78%

11.1 Using Mental Methods

Some percentages are easier to find because they are simple fractions. The purpose of using mental methods is to accelerate working out percentages of simple values.

I have three questions to ease your understanding.
                                                     

Questions:

1. 35% of 84

= 10% + 10% + 10% + 5% = 35%

= 8,4 + 8,4 + 8,4 + 4,2 = 29,4.

2. 49% of 230

= 50% - 1% = 49%

= 115 - 23 = 92.

3.   26% of 78 = 20,28  use this fact to find 52% of $78

You can see that the value that we are working out is the same as the fact which is 78.

The one that we have to focus is the percentage. The fact is 26%. While in the question is 52%.

52-26 = 26%

So first we have to work out the 26 % of 78 and then add the result to the answer in the fact box.

=> 20,28 + 20,28 = 40,56

So the answer is $40,56