How do you give an example of the sale price of an item and the total cost including sales tax if the tax rate is 5.75% and the item is 25% off?

Example of a Problem:

Let's say there is a pair of pants which are regularly priced for #$20#.

The store is having a 25% off sale for all items in the store.

The sales tax on all items in the store is 5.75%

How much do you need to pay for the pair of pants?

Solution to the Problem:

The formula for the cost of the item on sale is:

#c = p - (s * p)#

Where:

#c# is the sale price of the items. What we will solve for.

#p# is the regular price of the item. $20 for this problem.

#s# is the sales percentage. 25% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 25% can be written as #25/100#.

Substituting and calculating #c# gives:

#c = $20 - (25/100 * $20)#

#c = $20 - ($500)/100#

#c = $20 - $5#

#c = $15#

Now, to find the total you would pay, with tax, we use this formula:

#t = c + (r xx c)#

Where:

#t# is the total amount paid with tax. What we are solving for.

#c# is the cost of the item. #$15# from the above calculation.

#r# is the tax rate. 5.75% for this problem. Again, "percent" or "%" means "out of 100" or "per 100", Therefore 5.75% can be written as #5.75/100#.

Substituting into this formula and calculating #t# gives:

#t = $15 + (5.75/100 xx $15)#

#t = $15 + ($86.25)/100#

#t = $15 + $0.86# rounded to the nearest penny.

#t = $15.86#

The total paid for the pants after the sale and tax are taken into account is: #color(red)($15.86)#