Mary is buying several items that cost $128.25 total. She is using a store coupon for 35% off her purchases. She has to pay 4% sales tax. Calculate the total cost of the items.

Question

holsteremission · Answer

$$\mathrm{total}=\mathrm{subtotal}\times(1-\mathrm{discount})\times(1+\mathrm{tax})$$Why? Discounts are taken into account before tax. So if the subtotal is $x$ and the discount is $d$, then you remove $dx$ from $x$, i.e. $x-dx=x(1-d)=x^*$, where $x^*$ denotes the new subtotal. The sales tax $s$ then kicks in, adding $s$ times the value of the subtotal, i.e. $x^*+sx^*=x^*(1+s)=x(1-d)(1+s)$.

mathstudent55 · Answer

The items cost $128.25 before the discount and before the tax.

To find the discounted price, first, subtract 35% from 100% to get 65%.
65% is the same as 0.65 as a decimal.
Then multiply the cost before discount and taxes by 0.65.

To add the tax, first add 100% and 4% to get 104%.
104% is the same as 1.04 as a decimal.
Then multiply the discounted price by 1.04.