Question 1123865
the sweater is on sale for $80.00


take the discount first and then pay the sales tax equals .8 * $80 * 1.07


pay the sales tax first and then take the discount equals $80 * 1.07 * .8


i think it will wind up being the same.


breaking it down into more detail.


the price is $80.00
20% off is .2 * $80.00 = $16.00
$80.00 - $16.00 = $64 sale price
7% sales tax on $64 = $4.48.
$64 + $4.48 = $68.48 total


the price is $80.00
7% sales tax on $80 = $5.60
$80.00 + $5.60 = $85.60
20% off is .2 * $85.60 = $17.12
$85.60 - $17.12 = $68.48 total


the total price is the same.


this has to do with the commutative law of multiplication that states that a * b is the same as b * a.


20% discount is the same as multiplying the price by .8
7% sales tax is the same as multiplying the price by 1.07


.8 * $80 * 1.07 is the same as 1.07 * $80 * .8


the .8 factor is achieved in the following manner.


x - .2 * x = x * (1 - .2) = x * .8 = .8 * x


the 1.07 factor is achieved in the following manner.


x + .07 * x = x * (1 + .07) = x * 1.07 = 1.07 * x