Let  be the value of all books purchased. First, a discount of  is applied to , then a tax of  is applied to get . We can then write the following equation:

The value of the books purchased is .

Basically, the customers who buy through the third party merchant buy tickets at a  discount. As customers who book through the airline company pay the full price, customers who buy through the third party merchant would then pay  of the full price since, they benefit from a  discount.

A customer booking the same flight through the third-party merchant would then pay  for that flight.

This result is equivalent to using the percent of change formula:

First we find how much money Mary will save with the discount. If the sweater is 25% off, then the amount saved will be 25% of the original price:

0.25($42.00) = $10.50

Now we subtract the discount from the original price of the sweater to find the price Mary will pay at the register:

$42.00 - $10.50 = $31.50

At Carter Brothers Furniture, the chair sells for 30% off the normal price of $600. This is 70% of $600, or

At Elm Street Furniture, the chair sells for 20% off the normal price of $575. This is 80% of $575, or

At General Grant Furniture, the chair sells for 10% off the normal price of $560. This is 90% of $560, or

At Irving Furniture, the chair sells for 40% off the normal price of $720. This is 60% of $720, or 

At King of Furniture the chair sells for $540. 

Carter Brothers Furniture is selling the chair for the lowest price, and it is where Brian should go.

Call  the price before discount or tax. The amount of the discount is 20% of this, so the price after discount but before tax is  of this, or  of ; this is .

Similarly, the amount paid will be this price plus 5% of this as tax, or  of . 105% is , so the final amount paid is 

Therefore, 

and 

To calculate discounts, it is often easiest to write out an equation. Before we do that, though, we need to make note of one detail. Jenkins receives a 15% discount on his bike. This means his bike is 85% of the original cost. So, we can set up the following equation:

Here,  is our original price and  is our sale price. Plug in 635 for  and divide over the 0.85 to get:

We can round this to $747. We are not done yet, though, because we need to find the dollar amount saved. To find that , simply take the difference between the sale price and the original price.

Our answer is $112.

If the jeans are originally $40 and are 40% off, then Tom will pay 40% of $40 less than the original price for them. This gives us:

Set up a short equation to get our answer. We know that if we take  off of the original price, we get . That means  is  of the original price. So:

Solve for , the original price of the computer:

The computer's original price was .

To solve this problem, we should use the decrease/increase formula: .

To find the change in the price we simply calculate the difference of the new price minus the original price, which gives us .

Then we just need to divide this change in value by the original value, wich gives us or , which is  discount.

By pluging in the values we have in the percent change formula ,

we can see that my grade will increase by  .