Question

Dalia buys a winter jacket at a used clothing store that costs $30. She lives in Idaho, where the sales tax is 6%. Write an equation that represents the total cost, c, of any item bought in Idaho whose price is p.

Dalia buys a backpack at a different store in Idaho. It is on sale for 30% off. Dalia pays $33.39 total (including sales tax). What was the original price of the backpack?

Answer 1

Explanation:

Discussion

Question One

The first question is just to derive a formula that represents the cost of anything bought in Idaho.

c = p + 6/100 * p

c = p + 0.6 * p

c = 1.06 p

Question Two

The second question requires an entirely different formula. You don't use the first formula. You just use it's idea. Further, you take the sales tax only when you know how much money has exchanged hands.

c = (p - 30/100 p) + 6/100*(p - 30/100 * p)

c = (p - 0.3p) + 0.06* (p - 0.3p)

c = 0.7 p + 0.06*(0.7p) Combine the right side

c = 0.7p + 0.042p Combine

c = 0.742p

33.39 = 0.742p Divide by 0.742

33.39/0,742 = p

p = 45 dollars

The original cost was 45 dollars