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GCSE: AQA Unit 1 [calculator allowed]
Ratio and Percentage Examples
Key ratio examples
Example 1
Jack and Jill share some money in the ratio 3:11
If Jill receives £357.50, how much does Jack receive?
We can lay it out in a table
Jack 

Jill 



So Jack receives:
Example 2
Dodgy Dan sells old and new cars in the ratio 17:15. What percentage
of the cars he sells are new cars?
a) Add up the parts
b) So the percentage of
new cars is
Key Percentage Examples
Example set 1: Quick percentages on a calculator


Increase £230 by 15% 100%+15%=115% so we
do: 
Decrease £432 by 22% 100%22%=78% so we
do: 
Example set 2: finding percentage changes
The number of people
in a school goes up from 620 to 715. What is the percentage increase? a)
Increase
is 715620=95 b)
So
percentage increase is: Generally, we do: 
Dodgy Dan hopes to
increase his sales by 17%. They go up from 23,000 to 26,500. Has he met his
target? a)
The
increase is 26,50023,000=3500 b)
So
percentage increase is: No, he has not met
his target! 
Example set 3: Exponential growth/compound interest
Peter invests £300 at
an interest rate of 7%. How much does he have after 8 years? Each year sees an
increase of 7%. 100% + 7% = 107%, so
we need to multiply by 1.07 for each year. So after eight years
he has: NB: Observe how we
have used the power button rather than multiply by 1.07 eight times 
Example set 4: reverse percentages
Sam buys an antique
and a year later it has increased by 13% to £395.50. How much was it worth
originally. To increase by 13% we
know we have to multiply by 1.13. However, we are
looking for the price BEFORE the increase. To find this original price we
must reverse this change BY DIVIDING the NEW VALUE by 1.13 
VAT is added at 20%.
A shopkeeper is selling a TV for £4674 (including VAT) How much VAT has been
added? To increase by 20% we
know we have to multiply by 1.20 Therefore, the price BEFORE
VAT was added must have been: So, the amount of VAT
is £4674  £3895 = £779 