A pair of shoes usually sells for $63. If the shoes are 30% off, and sales tax is 8%, what is the total price of the shoes, including tax?

Work Shown:

The discount is 30%, so you still have to pay 70% (because 100% - 30% = 70%)

70% = 0.70

Multiplying by 0.70 represents a decrease of 30%

Multiplying by 1.08 represents an increase of 8%, which is where the tax comes in.

The multipliers are: 0.70 and 1.08

So,

final price = (original price)*(discount multiplier)*(tax multiplier)

final price = 63*0.70*1.08

final price = 47.628

final price = 47.63

With this method, we can chain multiple discounts and/or taxes, fees etc in a very quick efficient manner.

The (slightly) longer route might look like this

original price = 63

discount = 30% of original price = 0.30*63 = 18.90

price after discount = (original price) - (discount) = 63 - 18.90 = 44.10

note how this is the longer way of saying 63*0.70 = 44.10

Now apply the tax

tax = 8% of 44.10 = 0.08*44.10 = 3.528

final price after tax = 44.10 + 3.528 = 47.628 = 47.63

or you can say,

1.08*44.10 = 47.628 = 47.63

to get the same answer.