# Percentage increase and discount

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O increase and the percentage discount are applied to the sale price of a commodity. Before changing the value of a product, variables such as inflation, supply and demand are taken into account.

The calculation for increase is given by the following formula:

x + w%. x = x + P . x
100

x = It is the value of the merchandise or product in reais (R\$);
p = is the percentage of increase that affects the product, which, in this case, is x;
+ = The plus sign (+) is what represents the increase.
% = this symbol (%) can be represented as a fraction: 1 .
100

The structuring of the formula of discountis as follows:

x – p%. x = x - P . x
100

x = It is the value of the merchandise or product in reais (R\$);
p = is the percentage of increase that affects the product, which, in this case, is x;
- = the minus sign (-) represents the discount;
% = this symbol (%) can be represented as a fraction 1 .
100

Now let's solve two examples:

Example 1

Ana wants to buy a new television to watch the Olympics in high resolution. She decides to buy a Smart TV that is full HD. Before going to the physical store, she makes an internet consultation to research the price of the TV. She discovers that the value of the television is R\$1580.00. When going to the physical store, Ana is startled, which is actually a good surprise. The TV she wants to buy has a 30% discount. Calculate how much Ana will pay for television.

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This is an example of a percentage discount. Therefore, we must use the formula:

x - p%. x = x - P . x
100

Data:

x = BRL 1580.00
p = 30% = 30
100

Resolution:

x - p%. x = x - P . x = 1580 - 30 . 1580 = 1580 – 47400 = 1580 – 474 = 1106
100 100 100

With the 30% discount, Ana will pay R\$1106.00 for the TV

Example 2

Alcir wants so much to buy a car that he even keeps the coins. On television, there are so many commercials talking about the reduction of the IPI (Tax on Industrialized Product) that every day he is encouraged to buy the car. During a year of savings, Alcir finds himself in a difficult situation, as dealerships are no longer offering the IPI discount, which was 18%. He had raised R\$21,000.00, but this money will no longer be enough to buy the car in cash. Calculate how much more money Alcir will need to buy the car.

In this example, we will use the formula for the percentage increase.

x + w%. x = x + P . x
100

Example data

x = BRL 21,000.00
p = 18% = 18
100

Example resolution

x + w%. x = x + P . x
100

21000 = x + 18.x
100

21000 = 100.x + 18.x
100 100

21000 = 82.x
100

21000,100 = 82.x

2100000 = x
82

x = 25609.75

The car that Alcir wants to buy now costs R\$ 25,609.75. To buy it, Alcir will have to save another R\$4,609.75

BRL 25,609.75 - BRL 21,000.00 = BRL 4,609.75

By Naysa Oliveira

Source: Brazil School - https://brasilescola.uol.com.br/matematica/aumento-desconto-percentual.htm

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