## Percentages

Percentage questions typically take one of three forms:

If a quantity increases (decreases) by x% what is the new quantity?

What is A as a percentage of B? or find the percentage increase (decrease).

If a price increases by x% and is now £A find the price before the increase.

I will illustrate these in turn.

If the price of a car is £6000 and it increases by 15% what is the new quantity?

Find 15% of

The new price is £6000+£900=£6900.

If the price of a car is £6000 and it increases by £1200 what is the new percentage increase?

Use the formula %

The new price is £7200. The percentage change is%.

If the price of a car increases by 10% and the new price is £13200 what was the original price?

Construct a Ratio Table and scale down from the new price to the original. Since the price increased by 10% the new price is 110% of the original. We have to scale down from 110% to 100%.

% | £ |

110 | 13200 |

100 | 12000 |

The scale factor from 110 to 100 isand this is the scale factor from the new to the original price: the original price is