If Phillip buys the shoes at Shoe festival, their cost including the discount will be 25% off $220, or 75% of $220. This will be

If he buys the shoes at Costless, he will pay $150 plus 8.5% tax - that is, he will pay 1.085 times $150, or

Phillip will save

buying at Costless.

Call  the price before the two discounts. The amount of the store discount is 15% of this; the final purchase price is , or , of the original price, so the price after the store discount, but before the employee discount, is .

Similarly, the price after the employee discount will be  of this, or

So

and, consequently,

 or 

Call  the price before the 15% discount. The amount of the discount is 15% of this; the final purchase price is , or , of the original price, so

 or 

A  discount implies that the discounted price is  of the original price; a tax means that  of the price will have to be paid. Let  be the original price.

We can now write an equation and solve for :

The formula to find the percentage change in the price is the following:

We plug the new price and the percentage of discount into the equation to determine the shirt's original price.

Let  be the original price:

Another approach is to think as the new price as  times the original price, since after the discount, the shirt costs only  of the original price. So:

John is supposed to save a total of  for the next year. Therefore, the difference between the sum of all his monthly premiums from the previous year and the sum of all his monthly premiums from the next year is .

Using the following formula:

We can see that  is the difference between his new annual payments and his original annual payments before the discount. The value of the annual payments is twelve times the monthly premium:

This means that John saves  due to the discount.

Another way to calculate the percentage of discount is to first find John's new monthly premium.

Let  be John's monthly premium after applying the discount:

The percentage of the safe driver discount is then:

The safe driver discount is 15.6% off his previous monthly premium.

Let  be the percentage of discount. If the store owner sells the t-shirts at the full price, his gross margin per t-shirt sold is:

The discounted price will be , and the cost of making a t-shirt remains the same.

We can write the following equation to find the percentage of discount if we reduce the gross margin per t-shirt by :

The store owner can offer a  discount if he is willing to reduce his gross margin by .

We need to algebraically model the cost per bracelet from the old supplier vs. the cost per bracelet from the new supplier, who is offering a "discount" on the cost of the bracelet from the old supplier. We know that if Jane orders from the new supplier, her gross profit will increase by , so we can model the situation as a percent increase and solve for a the missing variable of the discount the new supplier is offering on the cost of each bracelet from the old supplier.

Jane sells each bracelet for , and we are solving for the discount the new supplier is offering on the cost of each bracelet, which from the old supplier was . We can consider this as a percentage subtracted from the cost of each bracelet from the old supplier, .

Jane's profit when buying from her current supplier is:

If Jane buys from the new supplier, her profit will be:

Distributing the  and then combining like terms:

We can then write the percentage increase as:

The new supplier's price is  less than the current supplier.

We will use the formula for percentage of change.

Let  be the original price of the gallon of milk. The new price is , and the percentage of discount is .

The new price is  less than the original price of . Therefore, the new price is: